Methods and apparatus for reconstruction of volume data from projection data

• US 20050135664A1
• Filed: 12/23/2003
• Published: 06/23/2005
• Est. Priority Date: 12/23/2003
• Status: Active Grant

• Current Assignee: GE Medical Systems Global Technology Company LLC (GE Healthcare Technologies, Inc.)
• Original Assignee: GE Medical Systems Global Technology Company LLC (GE Healthcare Technologies, Inc.)
• Inventors: Claus, Bernhard Erich Hermann, Kaufhold, John Patrick
• Granted Patent: US 7,653,229 B2
• Time in Patent Office: Days
• US Class Current: 382/131
• CPC Class Codes: G06T 11/006 Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
• CPC Class Codes: G06T 2211/424 Iterative
• CPC Class Codes: G06T 2211/436 Limited angle

Abstract

Some configurations of method for reconstructing a volumetric image of an object include obtaining a tomosynthesis projection dataset of an object. The method also includes utilizing the tomosynthesis projection dataset and additional information about the object to minimize a selected energy function or functions to satisfy a selected set of constraints. Alternatively, constraints are applied to a reconstructed volumetric image in order to obtain an updated volumetric image. A 3D volume representative of the imaged object is thereby obtained in which each voxel is reconstructed and a correspondence indicated to a single one of the component material classes.

Claims

1. A method for reconstructing a volumetric image of an object comprising:

obtaining a tomosynthesis projection dataset of an object; and

utilizing the tomosynthesis projection dataset and additional information about the object, minimizing a selected energy function or functions to at least one of satisfy or arbitrate among a selected set of constraints to obtain a 3D volumetric image representative of the imaged object in which each voxel in the volumetric image corresponds to a single one component material class.

2. A method in accordance with claim 1 wherein the volumetric image is an N-ary volumetric image, and the selected energy function or functions comprises an energy functional which relates the N-ary volumetric image to a volumetric image of the object obtained by utilizing a different imaging modality.

3. A method in accordance with claim 1 wherein the object is an anatomical object, and the energy functional includes a shape energy term in which the N-ary volumetric image is constrained to contain material class anatomy shapes that are similar to a real anatomy.

4. A method in accordance with claim 3 wherein the material class anatomy shapes include ligaments and glands.

5. A method in accordance with claim 3 wherein the shape energy term penalizes a three dimensional morphology of the N-ary volumetric reconstruction.

6. A method in accordance with claim 1 wherein, for isolated voxels of a single material class surrounded by a plurality of other voxel labels, the isolated voxel is set to one of the surrounding labels.

7. A method in accordance with claim 1 wherein the energy functional is an overall conglomerate functional that has properties that are a function of a plurality of specific energy definitions.

9. A method in accordance with claim 1 further comprising setting at least one of said specific energy definitions to zero when it may be less than a tolerance value.

10. A method in accordance with claim 1 wherein said energy functional comprises a plurality of terms selected from the group consisting of a projection domain fidelity constraint, a reconstructed volumetric image domain fidelity constraint, an edge-preserving smoothness constraint, an intensity model constraint, a boundary field model constraint, an intensity model probability constraint, a boundary field model probability constraint, a bias field constraint, an artifact minimizing constraint, a boundary property constraint, and combinations thereof.

11. A method in accordance with claim 10, wherein said energy functional comprises a projection domain fidelity constraint having an energy term to quantify reprojection consistency written as:

$\underset{\mathrm{Projections}}{\int <br><br>}<br><br>{\left(P<br><br>\left(v+G\right)-y\right)}^{\mathrm{q1}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>p$

where P(ν

+G) is the projection of the sum of the reconstructed volumetric image, ν

, and an artifact field, G, into the same space as the acquired projection images, y, and q1 is a scalar exponent.

12. A method in accordance with claim 10, wherein said energy functional comprises a projection domain fidelity constraint written as:

$\underset{\mathrm{Projections}}{\int <br><br>}<br><br>T<br><br>\left(v,G,y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>p$

where T is a penalty on some metric which differentiates the observed projections, y, from the expected projections from the joint estimate of ν and

G, where ν

is the reconstructed volumetric image, and G is an artifact field.

13. A method in accordance with claim 10, wherein said energy functional comprises a reconstructed volumetric image domain fidelity constraint written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>y_R-\left(v+G\right)<br><br>}^{\mathrm{q2}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

wherein y_R is an observation in the reconstructed volumetric image domain, ν

is the reconstructed volumetric image, G is an artifact field, and q2 is a scalar exponent.

14. A method in accordance with claim 13 wherein y_R is a min norm least squares solution of observed projections through projection operator P.

15. A method in accordance with claim 13 wherein said energy functional further penalizes deviations from reconstructed volumetric images from previous years or from other modalities.

16. A method in accordance with claim 10, wherein said energy functional comprises an edge-preserving smoothness constraint locally penalizing a derivative of an intensity value.

17. A method in accordance with claim 10, wherein said energy functional comprises an edge preserving smoothness constraint combining smoothing and edge preservation.

18. A method in accordance with claim 10, wherein said energy functional comprises an edge-preserving smoothness constraint written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{\left(1-s\right)}^{\mathrm{q3}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>\mathrm{\Omega <br><br>}<br><br>\left(\nabla <br><br>v,C\right)<br><br>}^{\mathrm{q4}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where s is an edge strength field between 0 and 1 (s˜

0 being smooth and s˜

1 being an edge), q3 is a scalar exponent, Ω

(x,y) is a weighting function on the local field x, conditioned on a curve in space, y, and {overscore (V)}ν

is the gradient of ν

, which itself is the reconstructed volumetric image, and q4 is a scalar exponent.

19. A method in accordance with claim 10, wherein said energy functional comprises an intensity model constraint penalizing any value in the reconstructed volumetric image that does not lie in a physically possible or probable range.

20. A method in accordance with claim 10, wherein said energy functional comprises an intensity model constraint utilizing the fact that linear attenuation coefficients for different locations within a reconstructed volumetric image are distinct, not mixed.

21. A method in accordance with claim 20 further comprising utilizing said intensity model constraint in combination with a prior model in which certain material classes are likely to be present.

22. A method in accordance with claim 10, wherein said energy functional comprises an intensity model constraint that penalizes large deviations from specific intensity levels, said intensity model constraint written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>\mathrm{\Phi <br><br>}<br><br>\left(v,\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q5}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where Φ

(ν

, μ

) is a function that takes the reconstructed volumetric image, ν

, into the intensity model domain, μ

, so that it may be compared to ν

, where μ

is a prior model of expected intensities in ν

, ν

is the reconstructed volumetric image, μ

is the spatially dependent intensity model, and q5 is a scalar exponent.

23. A method in accordance with claim 22, wherein, for a voxel at a given location coming from one of two different tissue classes, with means m₁ and m₂, respectively, the contribution to the energy functional at the given voxel location is larger for voxel intensity values at that location that are further from m₁ or m₂ compared to the contribution to the energy functional at that voxel if its intensity were closer to m₁ or m₂.

24. A method in accordance with claim 10 wherein said energy functional comprises a structural shape constraint that penalizes material class shapes that deviate significantly from expected physical shape characteristics of structures in the real anatomy.

25. A method in accordance with claim 24 used to reconstruct a volume of a breast, wherein μ

describes a breast composed of a plurality of structures embedded in a volume of otherwise fatty-equivalent tissue.

26. A method in accordance with claim 25 wherein the structures comprise the group consisting of fibrous structures, glands, Cooper'"'"'s ligaments, microcalcifications, fibroadenomas, architectural distortion, and combinations thereof.

27. A method in accordance with claim 10, wherein said energy functional comprises a boundary field model constraint to constrain properties of an edge field.

28. A method in accordance with claim 27 wherein said boundary field model constraint comprises an energy model written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>\mathrm{\Psi <br><br>}<br><br>\left(s,\mathrm{\sigma <br><br>}\right)<br><br>}^{\mathrm{q6}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where Ψ

(s, σ

) is a function that takes an estimated edge field, s, into the boundary model domain, σ

, so that it may be compared directly to σ

, s is the edge strength field, and σ

is a prior model of expected boundary properties, and q6 is a scalar exponent.

29. A method in accordance with claim 10 wherein said energy functional comprises an intensity model probability constraint.

30. A method in accordance with claim 29 wherein said intensity model probability constraint comprises an energy term written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>T<br><br>\left(\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q7}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where T(μ

) is a function that is large for unlikely models, μ

, and smaller for more likely models, μ

, μ

is the spatially dependent prior model on intensities of ν

, and q7 is a scalar exponent.

31. A method in accordance with claim 30 wherein μ

depends upon a volumetric image obtained with another modality.

32. A method in accordance with claim 30 wherein μ

depends upon a high-level representation of the volumetric image ν

.

33. A method in accordance with claim 32 wherein a high level representation of ν

comprises a convex hull.

34. A method in accordance with claim 32 wherein a high level representation of ν

includes an integral measure of squared intensity in a background of the image.

35. A method in accordance with claim 10 wherein said energy functional comprises a boundary field model probability constraint that constrains a prior model of an edge strength function.

36. A method in accordance with claim 35 wherein when it is known a priori that an edge is less likely to develop a prior model of the edge strength function that allowed the edge strength function to develop large edge strength values in a region of an image is penalized more than a prior model of the edge strength function that did not allow the edge strength function to develop edges in those regions.

37. A method in accordance with claim 35 wherein the boundary field model probability constraint comprises an energy function written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>\mathrm{\Lambda <br><br>}<br><br>\left(\mathrm{\sigma <br><br>}\right)<br><br>}^{\mathrm{q8}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where Λ

(σ

) is a function that is large for unlikely boundary field models, σ

, and smaller for more likely boundary field models, σ

, and q8 is a scalar exponent.

38. A method in accordance with claim 10 wherein said energy functional comprises a bias field constraint configured to source separate an artifact volumetric image from a real attenuation coefficient volumetric image.

39. A method in accordance with claim 38 wherein said bias field constraint comprises an energy function written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>M<br><br>\left(G\right)<br><br>}^{\mathrm{q9}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

M(G) is a function that is large for both unlikely artifact volumetric images, G, and for artifact volumetric images, G, that resemble true tissue structure, G is the artifact field, and q9 is a scalar exponent.

40. A method in accordance with claim 39 wherein M(G) is a measure of high frequency energy in G.

41. A method in accordance with claim 10 wherein said energy functional comprises an artifact minimizing constraint energy function.

42. A method in accordance with claim 41 wherein said artifact minimizing constraint energy function comprises an energy function written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>A<br><br>\left(v\right)<br><br>}^{\mathrm{q10}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where A(ν

) is a measure of the artifacts in ν

, ν

is the reconstructed volumetric image, and q10 is a scalar exponent.

43. A method in accordance with claim 42 wherein A(ν

) is large for reconstructions where copies of high-contrast structures are spread into adjacent planes of the reconstructed volumetric image, and smaller for reconstructed volumetric images where such an artifact is reduced.

44. A method in accordance with claim 10 wherein said energy functional comprises a boundary property constraint.

45. A method in accordance with claim 44 further comprising evolving a closed n-1 dimensional hypersurface embedded in an n-dimensional field under influence of an edge strength function and a curvature-dependent bending force, reaching an equilibrium of the hypersurface, and taking the equilibrium hypersurface as a boundary separating different material classes.

46. A method in accordance with claim 45 further incorporating an influence of a prior model on the hypersurface into the energy utilizing an energy function written as:

$\underset{\underset{\mathrm{Interface}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{Properties}}{\mathrm{Tissue}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{Surface}}}{\int <br><br>\int <br><br>}<br><br>{<br><br>Z<br><br>\left(C,C_{\mathrm{\mu <br><br>}}\right)<br><br>}^{\mathrm{q11}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>S$

where Z(C, C_μ

) is a function that measures a number of properties of the curve or surface, C, and computes some distance to another curve or surface, C_μ

;

C is the curve or surface in space, C_μ

is the model for the given material class surface interface and q11 is a scalar exponent.

47. A method in accordance with claim 46 wherein said distance to another curve or surface is selected from the group consisting of diffeomorphism, Hausdorff metric, and weighted parameter difference.

48. A method in accordance with claim 10 wherein said energy functional comprises an overall energy written as:

$E=\underset{i}{\sum <br><br>}<br><br>E_i<br><br>\left(v,s,G,C\right)$

where each component energy, E_i, is one of

$E_P<br><br>\left(v,G\right)=\mathrm{\eta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>\underset{\mathrm{Projections}}{\int <br><br>}<br><br>{\left(P<br><br>\left(v+G\right)-y\right)}^{\mathrm{q1}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>p$

where η

is a scalar to balance the influence of this term against other terms,

$\begin{array}{c}{E}_R<br><br>\left(v,s,G,C\right)=<br><br>\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>\mathrm{\chi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>y-v-G<br><br>}^{\mathrm{q2}}+{\mathrm{\alpha <br><br>}<br><br>\left(1-s\right)}^{\mathrm{q3}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>\mathrm{\Omega <br><br>}<br><br>\left(\nabla <br><br>v,C\right)<br><br>}^{\mathrm{q4}}+\\ <br><br>\mathrm{\beta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>\mathrm{\Phi <br><br>}<br><br>\left(v,\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q5}}+\mathrm{\gamma <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>\mathrm{\Psi <br><br>}<br><br>\left(s,\mathrm{\sigma <br><br>}\right)<br><br>}^{\mathrm{q6}}+\mathrm{\kappa <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>T<br><br>\left(\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q7}}+\\ <br><br>\mathrm{\lambda <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>\mathrm{\Lambda <br><br>}<br><br>\left(s\right)<br><br>}^{\mathrm{q8}}+\mathrm{\theta <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>M<br><br>\left(G\right)<br><br>}^{\mathrm{q9}}+\mathrm{\varpi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>A<br><br>\left(v\right)<br><br>}^{\mathrm{q10}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R\end{array}$

where χ

, α

, β

, γ

, κ

, λ

, θ

, and ω

are scalars that are used to balance the influence of this term internally as well as balance the influence of this term against other terms, and

$E_S<br><br>\left(C\right)=\underset{\underset{\underset{\mathrm{Interface}}{\mathrm{Surface}}}{\mathrm{Tissue}}}{\int <br><br>\int <br><br>}<br><br>\mathrm{\xi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>Z<br><br>\left(C,C_{\mathrm{\mu <br><br>}}\right)<br><br>}^{\mathrm{q11}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>S$

where ξ

is a scalar that is used to balance the influence of this term against the other terms.

49. A method in accordance with claim 48 wherein at least one scalar weight is chosen based on an initial volumetric image, Q0(x,y,z).

50. A method in accordance with claim 10 wherein said energy functional comprises an overall energy combined as at least one of a sum of separate energy terms, a multiplication of separate energy terms, in conjunction with other mappings (sigmoid), nonlinear combinations, min/max, and combinations thereof.

8. A method in accordance with claim I wherein at least one of said specific energy definitions may be bounded by a maximum value.

51. A method for reconstructing a volumetric image of an object, said method comprising:

acquiring a tomosynthesis projection dataset of an object;

preprocessing the projections to produce quantitative projections;

performing an initial reconstruction using the quantitative projections; and

choosing an energy definition to minimize, wherein the energy definition includes a term that constrains the reconstructed volumetric image to an N-ary or approximately N-ary composition of material classes.

52. A method in accordance with claim 51 further comprising performing an energy minimizing reconstruction utilizing the chosen energy definition to produce the volumetric image of the object.

53. A method in accordance with claim 52 wherein said preprocessing comprises at least one step selected from the group consisting of bad pixel correction, gain correction, scatter correction, a correction to remap intensities to reflect a quantitative measure of material class, and combinations thereof.

54. A method in accordance with claim 52 further comprising selecting parameters associated with the energy definition selection.

55. A method in accordance with claim 52 wherein the object is a breast.

56. A method in accordance with claim 52 wherein said preprocessing the projections to produce quantitative projections further comprises performing a scatter correction.

57. A method in accordance with claim 52 wherein the object is a breast, and said preprocessing the projections to produce quantitative projections further comprises utilizing calibration curves to produce the quantitative projections.

58. A method in accordance with claim 52 wherein the object is a breast, and said preprocessing the projections to produce quantitative projections further comprises determining at least one of an average percent glandular tissue for one or more projection images and an average percent glandular tissue over all projections.

59. A method in accordance with claim 52 wherein the object is a breast having a volume B, and wherein said performing an initial reconstruction comprises performing a filtered backprojection.

60. A method in accordance with claim 52 wherein said preprocessing the projections to produce quantitative projections further comprises at least one member of the group consisting of determining a line integral of an attenuation coefficient and determining a material class composition along a ray.

61. A method in accordance with claim 52 wherein an energy used in said energy minimization is selected to manage a plurality of constraints.

62. A method in accordance with claim 52 wherein an energy used in said energy minimization is selected to manage a plurality of objectives, including at least one objective selected from the list consisting of artifact rejection, strictly N-ary volumetric image, approximately N-ary volumetric image, and reprojection consistency.

63. A method in accordance with claim 52 further comprising utilizing prior knowledge of the object in said reconstruction so that said reconstructed volumetric image is essentially N-ary and each voxel thereof quantitatively reflects an actual material class of the object.

64. A method in accordance with claim 63 wherein the object is a breast, and said prior knowledge comprises an anatomy of the breast and x-ray properties of the breast.

65. A method for reconstructing a volumetric image of a breast, said method comprising:

acquiring a tomosynthesis projection dataset comprising a set of projection radiographs of a breast from different projection angles;

estimating a geometry of a three-dimensional volume that contains breast tissue to produce an air/tissue volumetric image, and thereby a volumetric image of the breast hull;

determining radiation pathlengths for each projection radiograph in the tomosynthesis projection dataset;

using the determined radiation pathlengths and tomosynthesis projection dataset to estimate a quantitative projection image for each projection radiograph;

determining an overall percentage glandular tissue for at least one of a plurality of quantitative projection images using said quantitative projection images;

using the set of quantitative projection images to estimate intensities of a volumetric image for voxels located within in the breast hull; and

utilizing said estimated intensities to determine an N-ary or approximately N-ary reconstructed volumetric image of the breast, wherein at least most voxels of said reconstructed volumetric image are labeled as one or the other member of the set of tissues consisting of fatty tissue and glandular tissue.

66. A method in accordance with claim 65 wherein said N-ary or approximately N-ary volumetric image is a strictly N-ary volumetric image, wherein all voxels of said volumetric image are labeled as one or the other member of the set of tissues consisting of fatty tissue and glandular tissue.

67. A method in accordance with claim 65 wherein said N-ary or approximately N-ary volumetric image is an approximately N-ary volumetric image, where most voxels of said reconstruction are labeled as one or the other member of the set of tissues consisting of fatty tissue and glandular tissue, and some voxels are labeled as one or more types of tissues different from said tissues in said set of tissues.

68. A method in accordance with claim 67 wherein said different tissues comprise microcalcifications.

69. A method in accordance with claim 68 further comprising:

finding microcalcifications in each image of the tomosynthesis projection dataset;

performing a three-dimensional reconstruction using the microcalcification detection images, wherein the reconstructed three dimensional volumetric image has essentially a zero mean background and signal only at locations of the microcalcifications;

finding individual microcalcifications in the three-dimensional volumetric image;

determining locations at which the microcalcifications manifested themselves in the projection images;

determining a microcalcification-free quantitative 3D volumetric image;

forming a corresponding 3D volumetric image using the microcalcification-free quantitative reconstruction; and

combining the constrained quantitative microcalcification-free volumetric image and the reconstructed three-dimensional reconstruction having essentially a zero mean background and signal only at locations of the microcalcifications.

70. A method in accordance with claim 69 further comprising iteratively enforcing the re-projection consistency constraint.

71. A method in accordance with claim 65 wherein said utilizing said estimated intensities to determine an N-ary or approximately N-ary volumetric image of the breast further comprises applying a plurality of constraints that constrain at least one member of the set consisting of anatomical morphology, intensities, and summary statistics of a quantitative volumetric image.

72. A method in accordance with claim 65 further comprising updating the N-ary or almost N-ary volumetric image using additional constraints.

73. A method in accordance with claim 65 wherein the estimating a quantitative projection image comprises using at least one of calibration curves, compressed breast thickness and x-ray technique.

74. An apparatus for producing a reconstructed volumetric image of an object, said apparatus comprising a radiation source, a detector, an image processor and a computer, wherein said image processor is not necessarily a separate component from said computer, said apparatus configured to:

obtain a tomosynthesis projection dataset of an object; and

utilize the tomosynthesis projection dataset and additional information about the object to minimize a selected energy function or functions to at least one of satisfy or arbitrate among a selected set of constraints to obtain a volumetric image in which each voxel is assigned a specific component material class.

75. An apparatus in accordance with claim 74 wherein the volumetric image is an N-ary volumetric image, and the selected energy function or functions comprises an energy functional which relates the N-ary volumetric to a volumetric image of the object obtained by utilizing a different imaging modality.

76. An apparatus in accordance with claim 75 wherein the object is an anatomical object, and the energy functional includes a shape energy term in which the N-ary volumetric image is constrained to contain material class anatomy shapes that are similar to a real anatomy.

77. An apparatus in accordance with claim 76 wherein the material class anatomy shapes include ligaments and glands.

78. An apparatus in accordance with claim 76 wherein the shape energy term penalizes a three dimensional morphology of the N-ary volumetric reconstruction.

79. An apparatus in accordance with claim 75 wherein, for isolated voxels of a single material class surrounded by a plurality of other voxel labels, the isolated voxel is set to one of the surrounding labels.

80. An apparatus in accordance with claim 75 wherein the energy functional is an overall conglomerate functional that has properties that are a function of a plurality of specific energy definitions.

81. An apparatus in accordance with claim 80 wherein at least one of said specific energy definitions may be bounded by a maximum value.

82. An apparatus in accordance with claim 80 further configured to set at least one of said specific energy definitions to zero when it may be less than a tolerance value.

83. An apparatus in accordance with claim 75 wherein said energy functional comprises a plurality of terms selected from the group consisting of a projection domain fidelity constraint, a reconstructed volumetric image domain fidelity constraint, an edge-preserving smoothness constraint, an intensity model constraint, a boundary field model constraint, an intensity model probability constraint, a boundary field model probability constraint, a bias field constraint, an artifact minimizing constraint, a boundary property constraint, and combinations thereof.

84. An apparatus in accordance with claim 83, wherein said energy functional comprises a projection domain fidelity constraint having an energy term to quantify reprojection consistency written as:

$\underset{\mathrm{Projections}}{\int <br><br>}<br><br>{\left(P<br><br>\left(v+G\right)-y\right)}^{\mathrm{q1}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>p$

where P(ν

+G) is the projection of the sum of the reconstructed volumetric image , ν

, and an artifact field, G, into the same space as the acquired projection images, y, and q1 is a scalar exponent.

85. An apparatus in accordance with claim 83, wherein said energy functional comprises a projection domain fidelity constraint written as:

$\underset{\mathrm{Projections}}{\int <br><br>}<br><br>T<br><br>\left(v,G,y\right)<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>p$

where T is a penalty on some metric which differentiates the observed projections, y, from the expected projections from the joint estimate of ν and

G, where ν

is the reconstructed volumetric image, and G is an artifact field.

86. An apparatus in accordance with claim 83, wherein said energy functional comprises a reconstructed volumetric image domain fidelity constraint written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>\mathrm{\chi <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>y_R-\left(v+G\right)<br><br>}^{\mathrm{q2}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

wherein y_R is an observation in the reconstructed volumetric image domain, ν

is the reconstructed volumetric image, G is an artifact field, and q2 is a scalar exponent.

87. An apparatus in accordance with claim 86 wherein y_R is a min norm least squares solution of observed projections through projection operator P.

88. An apparatus in accordance with claim 86 wherein said energy functional further penalizes deviations from reconstructed volumetric images from previous years or from other modalities.

89. An apparatus in accordance with claim 83, wherein said energy functional comprises an edge-preserving smoothness constraint locally penalizing a derivative of an intensity value.

90. An apparatus in accordance with claim 83, wherein said energy functional comprises an edge preserving smoothness constraint combining smoothing and edge preservation.

91. An apparatus in accordance with claim 83, wherein said energy functional comprises an edge-preserving smoothness constraint written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{\left(1-s\right)}^{\mathrm{q3}}<br><br>\text{\hspace{1em}<br><br>}<br><br>{<br><br>\mathrm{\Omega <br><br>}<br><br>\left(\nabla <br><br>v,C\right)<br><br>}^{\mathrm{q4}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where s is an edge strength field between 0 and 1 (s˜

0 being smooth and s˜

1 being an edge), q3 is a scalar exponent, Ω

(x,y) is a weighting function on the local field x, conditioned on a curve in space, y, and {overscore (V)}ν

is the gradient of ν

, which itself is the reconstructed volumetric image, and q4 is a scalar exponent.

92. An apparatus in accordance with claim 83, wherein said energy functional comprises an intensity model constraint penalizing any value in the reconstructed volumetric image that does not lie in a physically possible or probable range.

93. An apparatus in accordance with claim 83, wherein said energy functional comprises an intensity model constraint utilizing the fact that linear attenuation coefficients for different locations within a reconstructed volumetric image are distinct, not mixed.

94. An apparatus in accordance with claim 93 further configured to utilize said intensity model constraint in combination with a prior model in which certain material classes are likely to be present.

95. An apparatus in accordance with claim 83, wherein said energy functional comprises an intensity model constraint that penalizes large deviations from specific intensity levels, said intensity model constraint written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>\mathrm{\Phi <br><br>}<br><br>\left(v,\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q5}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where Φ

(ν

,μ

) is a function that takes the reconstructed volumetric image, ν

, into the intensity model domain, μ

, so that it may be compared to ν

, where μ

is a prior model of expected intensities in ν

, ν

is the reconstructed volumetric image, μ

is the spatially dependent intensity model, and q5 is a scalar exponent.

96. An apparatus in accordance with claim 95, wherein, for a voxel at a given location coming from one of two different tissue classes, with means m₁ and M₂, respectively, the contribution to the energy functional at the given voxel location is larger for voxel intensity values at that location that are further from m₁ or m2 compared to the contribution to the energy functional at that voxel if its intensity were closer to m₁ or m₂.

97. An apparatus in accordance with claim 83 wherein said energy functional comprises a structural shape constraint that penalizes material class shapes that deviate significantly from expected physical shape characteristics of structures in the real anatomy.

98. An apparatus in accordance with claim 97 used to reconstruct a volume of a breast, wherein μ

describes a breast composed of a plurality of structures embedded in a volume of otherwise fatty-equivalent tissue.

99. An apparatus in accordance with claim 98 wherein the structures comprise the group consisting of fibrous structures, glands, Cooper'"'"'s ligaments, microcalcifications, fibroadenomas, architectural distortion, and combinations thereof.

100. An apparatus in accordance with claim 83, wherein said energy functional comprises a boundary field model constraint to constrain properties of an edge field.

101. An apparatus in accordance with claim 100 wherein said boundary field model constraint comprises an energy model written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>\mathrm{\Psi <br><br>}<br><br>\left(s,\mathrm{\sigma <br><br>}\right)<br><br>}^{\mathrm{q6}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where Ψ

(s, σ

) is a function that takes an estimated edge field, s, into the boundary model domain, σ

, so that it may be compared directly to σ

, s is the edge strength field, and σ

is a prior model of expected boundary properties, and q6 is a scalar exponent.

102. An apparatus in accordance with claim 83, wherein said energy functional comprises an intensity model probability constraint.

103. An apparatus in accordance with claim 102 wherein said intensity model probability constraint comprises an energy term written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>T<br><br>\left(\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q7}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where T(μ

) is a function that is large for unlikely models, μ

, and smaller for more likely models, μ

, μ

is the spatially dependent prior model on intensities of ν

, and q7 is a scalar exponent.

104. An apparatus in accordance with claim 103 wherein μ

depends upon a volumetric image obtained with another modality.

105. An apparatus in accordance with claim 103 wherein μ

depends upon a high-level representation of the volumetric image ν

.

106. An apparatus in accordance with claim 105 wherein a high level representation of ν

comprises a convex hull.

107. An apparatus in accordance with claim 105 wherein a high level representation of ν

includes an integral measure of squared intensity in a background of the image.

108. An apparatus in accordance with claim 83, wherein said energy functional comprises a boundary field model probability constraint that constrains a prior model of an edge strength function.

109. An apparatus in accordance with claim 108 wherein when it is known a priori that an edge is less likely to develop a prior model of the edge strength function that allowed the edge strength function to develop large edge strength values in a region of an image is penalized more than a prior model of the edge strength function that did not allow the edge strength function to develop edges in those regions.

110. An apparatus in accordance with claim 108 wherein the boundary field model probability constraint comprises an energy function written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>\mathrm{\Lambda <br><br>}<br><br>\left(\mathrm{\sigma <br><br>}\right)<br><br>}^{\mathrm{q8}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

where Λ

(σ

) is a function that is large for unlikely boundary field models, σ

, and smaller for more likely boundary field models, σ

r, σ

is the boundary field, and q8 is a scalar exponent.

111. An apparatus in accordance with claim 83, wherein said energy functional comprises a bias field constraint configured to source separate an artifact volumetric image from a real attenuation coefficient volumetric image.

112. An apparatus in accordance with claim 111 wherein said bias field constraint comprises an energy function written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>M<br><br>\left(G\right)<br><br>}^{\mathrm{q9}}<br><br>\text{\hspace{1em}<br><br>}<br><br>d<br><br>R$

M(G) is a function that is large for both unlikely artifact volumetric images, G, and for artifact volumetric images, G, that resemble true tissue structure, G is the artifact field, and q9 is a scalar exponent.

113. An apparatus in accordance with claim 112 wherein M(G) is a measure of high frequency energy in G.

114. An apparatus in accordance with claim 83, wherein said energy functional comprises an artifact minimizing constraint energy function.

115. An apparatus in accordance with claim 114 wherein said artifact minimizing constraint energy function comprises an energy function written as:

$\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>{<br><br>A<br><br>\left(v\right)<br><br>}^{\mathrm{q10}}<br><br>d<br><br>R$

where A(ν

) is a measure of the artifacts in ν

, ν

is the reconstructed volumetric image, and q10 is a scalar exponent.

116. An apparatus in accordance with claim 115 wherein A(μ

) is large for reconstructions where copies of the high-contrast structures are spread into adjacent planes of the reconstructed volumetric image, and smaller for reconstructed volumetric images where such an artifact is reduced.

117. An apparatus in accordance with claim 83, wherein said energy functional comprises a boundary property constraint.

118. An apparatus in accordance with claim 117 further configured to evolve a closed n-i dimensional hypersurface embedded in an n-dimensional field under influence of an edge strength function and a curvature-dependent bending force, reach an equilibrium of the hypersurface, and take the equilibrium hypersurface as a boundary separating different material classes.

119. An apparatus in accordance with claim 118 further incorporating an influence of a prior model on the hypersurface into the energy utilizing an energy function written as:

$\underset{\mathrm{Interface}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{Properties}}{\underset{\mathrm{Tissue}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{Surface}}{\int <br><br>\int <br><br>}}<br><br>{<br><br>Z<br><br>\left(C,C_{\mathrm{\mu <br><br>}}\right)<br><br>}^{\mathrm{q11}}<br><br>d<br><br>S$

where Z(C, C_μ

) is a function that measures a number of properties of the curve or surface, C, and computes some distance to another curve or surface, C_μ

;

C is the curve or surface in space, C_μ

is the model for the given material class surface interface and q11 is a scalar exponent.

120. An apparatus in accordance with claim 119 wherein said distance to another curve or surface is selected from the group consisting of diffeomorphism, Hausdorff metric, and weighted parameter difference.

121. An apparatus in accordance with claim 83, wherein said energy functional comprises an overall energy written as:

$E=\underset{i}{\sum <br><br>}<br><br>E_i<br><br>\left(v,s,G,C\right)$

where each component energy, E_i, is one of

$E_P<br><br>\left(v,G\right)=\mathrm{\eta <br><br>}<br><br>\underset{\mathrm{Projections}}{\int <br><br>}<br><br>{\left(P<br><br>\left(v+G\right)-y\right)}^{\mathrm{q1}}<br><br>d<br><br>p$

where η

is a scalar to balance the influence of this term against other terms,

$\begin{array}{c}{E}_R<br><br>\left(v,s,G,C\right)=\underset{\mathrm{Regions}}{\int <br><br>\int <br><br>}<br><br>\mathrm{\chi <br><br>}<br><br>{<br><br>y-v-G<br><br>}^{\mathrm{q2}}+{\mathrm{\alpha <br><br>}<br><br>\left(1-s\right)}^{\mathrm{q3}}<br><br>{<br><br>\mathrm{\Omega <br><br>}<br><br>\left(\nabla <br><br>v,C\right)<br><br>}^{\mathrm{q4}}+\\ {\text{\hspace{1em}<br><br>}<br><br>\mathrm{\beta <br><br>}<br><br>{<br><br>\mathrm{\Phi <br><br>}<br><br>\left(v,\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q5}}+\mathrm{\gamma <br><br>}<br><br><br><br>\mathrm{\Psi <br><br>}<br><br>\left(s,\mathrm{\sigma <br><br>}\right)<br><br>}^{\mathrm{q6}}+\mathrm{\kappa <br><br>}<br><br>{<br><br>T<br><br>\left(\mathrm{\mu <br><br>}\right)<br><br>}^{\mathrm{q7}}+\\ \text{\hspace{1em}<br><br>}<br><br>\mathrm{\lambda <br><br>}<br><br>{<br><br>\mathrm{\Lambda <br><br>}<br><br>\left(s\right)<br><br>}^{\mathrm{q8}}+\mathrm{\theta <br><br>}<br><br>{<br><br>M<br><br>\left(G\right)<br><br>}^{\mathrm{q9}}+\mathrm{\varpi <br><br>}<br><br>{<br><br>A<br><br>\left(v\right)<br><br>}^{\mathrm{q10}}<br><br>d<br><br>R\end{array}$

where χ

, α

, β

, γ

, κ

, λ

, θ

, and ω

are scalars that are used to balance the influence of this term internally as well as balance the influence of this term against other terms, and

$E_S<br><br>\left(C\right)=\underset{\underset{\underset{\mathrm{Interface}}{\mathrm{Surface}}}{\mathrm{Tissue}}}{\int <br><br>\int <br><br>}<br><br>\mathrm{\xi <br><br>}<br><br>{<br><br>Z<br><br>\left(C,C_{\mathrm{\mu <br><br>}}\right)<br><br>}^{\mathrm{q11}}<br><br>d<br><br>S$

where ξ

is a scalar that is used to balance the influence of this term against the other terms.

122. An apparatus in accordance with claim 83, wherein said energy functional comprises an overall energy combined as at least one of a sum of separate energy terms, a multiplication of separate energy terms, in conjunction with other mappings (sigmoid), nonlinear combinations, min/max, and combinations thereof.

123. An apparatus for producing a reconstructed volumetric image of an object, said apparatus comprising a radiation source, a detector, an image processor and a computer, wherein said image processor is not necessarily a separate component from said computer, said apparatus configured to:

acquire projections of an object;

preprocess the projections to produce quantitative projections;

perform an initial reconstruction using the quantitative projections; and

choose an energy definition to minimize, wherein the energy definition includes a term that constrains the reconstructed volume to an N-ary or approximately N-ary composition of material classes.

124. An apparatus in accordance with claim 123 further configured to perform an energy minimizing reconstruction utilizing the chosen energy definition to produce the volumetric image of the object.

125. An apparatus in accordance with claim 124 wherein said preprocessing comprises at least one process selected from the group consisting of bad pixel correction, gain correction, scatter correction, a correction to remap intensities to reflect a quantitative measure of material class, and combinations thereof.

126. An apparatus in accordance with claim 124 further configured to select parameters for associated with the energy definition selection.

127. An apparatus in accordance with claim 124 configured to acquire projections of a breast.

128. An apparatus in accordance with claim 124 wherein to preprocess the projections to produce quantitative projections, said apparatus is further configured to perform a scatter correction.

129. An apparatus in accordance with claim 124 configured to acquire projections of a breast, and to preprocess the projections to produce quantitative projections, said apparatus is further configured to utilize calibration curves to produce the quantitative projections.

130. An apparatus in accordance with claim 124 configured to acquire projections of a breast, and to preprocess the projections to produce quantitative projections, said apparatus is further configured to determine an average percent glandular tissue for each projection and an average percent glandular tissue over all projections.

131. An apparatus in accordance with claim 124 configured to acquire projections of a breast having a volume B, and wherein said the reconstruction comprises a filtered backprojection.

132. An apparatus in accordance with claim 124 wherein to preprocess the projections to produce quantitative projections said apparatus is further configured to perform at least one member of the group consisting of determining a line integral of an attenuation coefficient and a material class composition along a ray.

133. An apparatus in accordance with claim 124 wherein an energy used in said energy minimization is selected to manage a minimization of a plurality of constraints.

134. An apparatus in accordance with claim 124 wherein an energy used in said energy minimization is selected to manage a plurality of objectives, including at least one objective selected from the list consisting of artifact rejection, approximately N-ary tissue reconstruction, and reprojection consistency.

135. An apparatus in accordance with claim 124 further configured to utilize prior knowledge of the object in said reconstruction so that said reconstruction is essentially N-ary and quantitatively reflects an actual material class of the object.

136. An apparatus in accordance with claim 135 configured to reconstruct an image of a breast, and said prior knowledge comprises an anatomy of the breast and x-ray properties of the breast.

137. An apparatus for producing a reconstructed volumetric image of a breast, said apparatus comprising a radiation source, a detector, an image processor and a computer, wherein said image processor is not necessarily a separate component from said computer, said apparatus configured to:

acquire a tomosynthesis projection dataset comprising a set of projection radiographs of a breast from different projection angles;

estimate a geometry of a three-dimensional volume that contains breast tissue to produce an air/tissue reconstruction of an image volume, and thereby a reconstruction of the breast hull;

determine radiation pathlengths for each projection radiograph in the tomosynthesis projection dataset;

use the determined radiation pathlengths and tomosynthesis projection dataset to estimate a percentage of glandular breast tissue material class for each projection radiograph, said estimate thereby producing a set of quantitative glandular projection estimates;

determine an overall percentage glandular tissue for a plurality of x-ray projection radiographs using said quantitative glandular projection estimates;

use the set of quantitative percentage glandular projection estimates to estimate intensities in the breast hull; and

utilize said estimated intensities to determine an N-ary or almost N-ary volumetric image of the breast, wherein at least most voxels of said reconstruction are labeled as one or the other member of the set of tissues consisting of fatty tissue and glandular tissue.

138. An apparatus in accordance with claim 137 wherein said N-ary or almost N-ary volumetric image is a strictly N-ary volumetric image, wherein all voxels of said reconstruction are labeled as one or the other member of the set of tissues consisting of fatty tissue and glandular tissue.

139. An apparatus in accordance with claim 137 wherein said N-ary or almost N-ary volumetric image is an almost N-ary volumetric image, where most voxels of said reconstruction are labeled as one or the other member of the set of tissues consisting of fatty tissue and glandular tissue, and some voxels are labeled as one or more types of tissues different from said tissues in said set of tissues.

140. An apparatus in accordance with claim 139 wherein said different tissues comprise microcalcifications.

141. An apparatus method in accordance with claim 140 further configured to:

find microcalcifications in each image of the tomosynthesis projection dataset;

perform a three-dimensional reconstruction using the microcalcification detection images, wherein the three dimensional reconstruction has essentially a zero mean background and signal only at locations of the microcalcifications;

find individual microcalcifications in the three-dimensional reconstruction;

determine locations at which the microcalcifications manifested themselves in projections;

determine a microcalcification-free quantitative reconstruction;

form a corresponding constrained reconstruction using the microcalcification-free quantitative reconstruction; and

combine the constrained quantitative volumetric tissue reconstruction and the reconstructed three-dimensional reconstruction having essentially a zero mean background and signal only at locations of the microcalcifications.

142. An apparatus in accordance with claim 141 further configured to iteratively enforce consistency with input data.

143. An apparatus in accordance with claim 137 wherein to utilize said estimated intensities to determine an N-ary or almost N-ary volumetric image of the breast, said apparatus is further configured to apply a plurality of constraints that constrain at least one member of the set consisting of anatomical morphology, intensities, and summary statistics of a qualitative reconstruction.

144. An apparatus in accordance with claim 137 further configured to perform a consistency check on the N-ary or almost N-ary volumetric image using additional constraints.

145. An apparatus in accordance with claim 137 wherein the prior knowledge comprises calibration curves, compressed breast thickness and x-ray technique.

146. A method for reconstructing a volumetric image of an object, said method comprising:

acquiring tomosynthesis dataset; and

utilizing the tomosynthesis dataset to determine a volumetric image of the object, wherein the volumetric image includes a plurality of voxels, and wherein each voxel corresponds to a material class.

147. A method in accordance with claim 146 wherein said reconstructing a volumetric image comprises processing a plurality of projection images such that the processed projection images are quantitative.

148. A method in accordance with claim 147 wherein said reconstructing a volumetric image comprises processing a plurality of projection images, wherein processing the plurality of projection images comprises at least one of performing a scatter correction, determining an average attenuation along an x-ray path, determining the material class composition for each pixel in the images, determining a breast hull air/tissue (AT) estimate, and performing a thickness compensation on the plurality of projection images.

149. A method in accordance with claim 147 wherein said reconstructing a volumetric image comprises determining an initial volumetric image of the object, and performing at least one update on the initial volumetric image of the object.

150. A method in accordance with claim 149 wherein said determining an initial volumetric image of the object comprises performing at least one of an FBP, a GFBP, a Fourier based reconstruction, MITS, DART, and an ART reconstruction.

151. A method in accordance with claim 149 wherein said reconstructing a volumetric image of the object comprises updating an estimate of the volumetric image using an energy functional.

152. A method in accordance with claim 149 wherein said updating an estimate of the volumetric image comprises updating an estimate of the volumetric image such that the update results in a decrease in the energy functional.

153. A method in accordance with claim 149 wherein said at least one update of an estimate of the volumetric image comprises updating the volumetric image such that at least one re-projection of the resulting volumetric image is constrained to be essentially identical to the corresponding projection image in the original tomosynthesis projection dataset.

154. A method in accordance with claim 150 wherein said performing at least one update on the initial volumetric image of the object further comprises applying a constraint to a previously determined estimate of the volumetric image of the object.

155. A method in accordance with claim 154 wherein said performing at least one update on the initial volumetric image of the object further comprises at least one of applying an N-ary material class constraint, constraining the volumetric image to the breast hull, constraining the intensities in the volumetric image to physically possible values, processing of volumetric image to remove artifacts, setting isolated voxels in volumetric image that correspond to one material class to the material class of voxels in a neighborhood.

156. A method in accordance with claim 146 wherein said utilizing the tomosynthesis dataset to determine a volumetric image of the object further comprises utilizing additional data to determine a volumetric image of the object.

157. A method in accordance with claim 156 wherein said utilizing additional data comprises utilizing data acquired from at least one of a tomosynthesis imaging system, an ultrasound imaging system, and a computed tomography imaging system.

158. A method in accordance with claim 156 wherein said utilizing additional data comprises utilizing at least one of a breast hull, a breast thickness, and summary composition statistics data to determine a volumetric image of the object.