Method for determining an optimally weighted wavelet transform based on supervised training for detection of microcalcifications in digital mammograms

• US 6,075,878 A
• Filed: 11/28/1997
• Issued: 06/13/2000
• Est. Priority Date: 11/28/1997
• Status: Expired due to Fees

• Current Assignee: ARCH Development Corporation (University of Chicago)
• Original Assignee: ARCH Development Corporation (University of Chicago)
• Inventors: Zhang, Wei, Yoshida, Hiroyuki, Nishikawa, Robert M., Doi, Kunio
• Primary Examiner(s): CHANG, JON CARLTON
• Application Number:
  US08/979,623
• Time in Patent Office: 928 Days
• Field of Search: 382/132, 382/248, 382/232, 378/37, 128/922
• US Class Current: 382/132
• CPC Class Codes: G06F 17/148 Wavelet transforms
• CPC Class Codes: G06T 7/0012 Biomedical image inspection

Abstract

A computer-aided diagnosis (CAD) method for detection of clustered microcalcifications in digital mammograms based on an image reconstruction using a substantially optimally weighted wavelet transform. Weights at individual scales of the wavelet transform are optimized based on a supervised learning method. In the learning method, an error function represents a difference between a desired output and a reconstructed image obtained from weighted wavelet coefficients of the wavelet transform for a given mammogram. The error function is then minimized by modifying the weights by means of a conjugate gradient algorithm. Performance of the optimally weighted wavelets was evaluated by means of receiver-operating characteristic (ROC) analysis which indicated that the present invention outperformed both a difference-image technique and partial reconstruction method currently used in CAD methods.

Claims

1. In a method for determining wavelet scale weighting coefficients, the improvement comprising:

performing supervised training, including wavelet transformation, iterative inverse wavelet transformation and error analysis, on at least one training image derived from sampled radiation to determine three or more non-zero wavelet scale weighting coefficients, comprising,

generating a teacher image based on a respective training image derived from sampled radiation, including

identifying in said teacher image true locations of indicia in said respective training image, and

defining a training-free zone around each of the identified true locations of said indicia in said teacher image; and

selecting said three or more non-zero wavelet scale weighting coefficients based on iterative inverse wavelet transformation and error analysis performed in relation to each said training-free zone defined in said teacher image;

wherein said step of selecting said three or more non-zero wavelet scale weighting coefficients includes the substeps of

a) selecting first candidate weighting coefficients,

b) generating a reconstructed training image based on the first candidate wavelet scale weighting coefficients and said respective training image,

c) determining a first error using said reconstructed image and said respective teacher image,

d) selecting second candidate weighting coefficients based on the first error and repeating steps b) and c) for the second candidate weighting coefficients until the error determined in step c) is within a specified error condition; and

wherein said substep of determining a first error includes the steps of;

determining a first error component based on a respective maximum value in each training-free zone in said at least one reconstructed image,

determining a second error component based on differences between intensity values of said respective teaching image and said reconstructed training image outside the training-free zones,

determining a ratio between a total number of said indicia identified and a number of pixels in the reconstructed training image outside the training-free zones,

providing a balanced error by multiplying said ratio to the second error component, and

calculating a total error in said at least one reconstructed image by combining the balanced error and the first error component.

2. The method according to claim 1, further comprising:

filtering an original image by applying a wavelet transformation decomposing said original image; and

reconstructing the decomposed original image by a weighted inverse wavelet transformation, utilizing said three or more non-zero wavelet scale weighting coefficients, applied to the decomposed original image.

3. The method according to claim 2, wherein said filtering step comprises:

decomposing the original image by means of a wavelet transformation into plural wavelet scales; and

reconstructing the decomposed original image, including,

applying said three or more non-zero wavelet scale weighting coefficients to respective of the plural wavelet scales of the decomposed original image, and

performing a weighted inverse wavelet transformation utilizing the plural wavelet scales of the decomposed original image.

4. The method according to claim 1, wherein said substep of selecting second candidate weighting coefficients includes the step of:

applying Powell'"'"'s conjugate gradient to said first error and said first candidate weighting coefficients to determine said second candidate weighting coefficients.

5. A computer readable medium on which is stored instructions that cause a computer system to determine wavelet scale weighting coefficients, by performing the step of:

performing supervised training, including wavelet transformation, iterative inverse wavelet transformation and error analysis, on at least one training image derived from sampled radiation to determine three or more non-zero wavelet scale weighting coefficients, comprising,

generating a teacher image based on a respective training image derived from sampled radiation, including

identifying in said teacher image true locations of indicia in said respective training image,

defining a training-free zone around each of the identified true locations of said indicia in said teacher image, and

selecting said three or more non-zero wavelet scale weighting coefficients based on iterative inverse wavelet transformation and error analysis performed in relation to each said training-free zone defined in said teacher image;

wherein said step of selecting said three or more non-zero wavelet scale weighting coefficients includes the substeps of,

a) selecting first candidate weighting coefficients,

b) generating a reconstructed training image based on the first candidate wavelet scale weighting coefficients and said respective training image,

c) determining a first error using said reconstructed image and said respective teacher image,

d) selecting second candidate weighting coefficients based on the first error and repeating steps b) and c) for the second candidate weighting coefficients until the error determined in step c) is within a specified error condition; and

wherein said substep of determining a first error includes the steps of;

determining a first error component based on a respective maximum value in each training-free zone in said at least one reconstructed image,

determining a second error component based on differences between intensity values of said respective teaching image and said reconstructed training image outside the training-free zones,

determining a ratio between a total number of said indicia identified and a number of pixels in the reconstructed training image outside the training-free zones,

providing a balanced error by multiplying said ratio to the second error component, and

calculating a total error in said at least one reconstructed image by combining the balanced error and the first error component.

6. The computer readable medium of claim 5, wherein the stored instructions further perform the steps of:

filtering an original image by applying a wavelet transformation decomposing said original image; and

reconstructing the decomposed original image by a weighted inverse wavelet transformation, utilizing said three or more non-zero wavelet scale weighting coefficients, applied to the decomposed original image.

7. The computer readable medium of claim 6, wherein said step of filtering includes the steps of:

decomposing the original image by means of a wavelet transformation into plural wavelet scales; and

reconstructing the decomposed original image, including,

applying said three or more non-zero wavelet scale weighting coefficients to respective of the plural wavelet scales of the decomposed original image, and

performing a weighted inverse wavelet transformation utilizing the plural wavelet scales of the decomposed original image.

8. The computer readable medium of claim 5, wherein the stored instructions for said substep of selecting second candidate weighting coefficients includes the step of:

applying Powell'"'"'s conjugate gradient to said first error and said first candidate weighting coefficients to determine said second candidate weighting coefficients.

9. In an apparatus for determining wavelet scale weighting coefficients, the improvement comprising:

means for performing supervised training, including wavelet transformation, iterative inverse wavelet transformation and error analysis, on at least one training image derived from sampled radiation to determine three or more non-zero wavelet scale weighting coefficients, comprising,

means for generating a teacher image based on a respective training image derived from sampled radiation, including

means for identifying in said teacher image true locations of indicia in said respective training image, and

means for defining a training-free zone around each of the identified true locations of said indicia in said teacher image; and

means for selecting said three or more non-zero wavelet scale weighting coefficients based on iterative inverse wavelet transformation and error analysis performed in relation to each said training-free zone defined in said teacher image;

wherein said means for selecting said three or more non-zero wavelet scale weighting coefficients comprises,

a) means for selecting first candidate weighting coefficients,

b) means for generating a reconstructed training image based on the first candidate wavelet scale weighting coefficients and said respective training image,

c) means for determining a first error using said reconstructed image and said respective teacher image, and

d) means for selecting second candidate weighting coefficients based on the first error and repeating use of said b) means for generating and said c) means for determining, for the second candidate weighting coefficients, until the error determined by said c) means for determining is within a specified error condition; and

wherein said means for determining a first error comprises,

means for determining a first error component based on a respective maximum value in each training-free zone in said at least one reconstructed image,

means for determining a second error component based on differences between intensity values of said at least one teaching image and said at least one reconstructed training image outside the training-free zones,

means for determining a ratio between a total number of said indicia identified and a number of pixels in the reconstructed training image outside the training-free zones,

means for providing a balanced error by multiplying said ratio to the second error component, and

means for calculating a total error in said at least one reconstructed image by combining the balanced error and the first error component.

10. The improvement according to claim 9, wherein said means for filtering comprises:

means for applying a wavelet transformation decomposing said original image; and

means for reconstructing the decomposed original image by a weighted inverse wavelet transformation, utilizing said three or more non-zero wavelet scale weighting coefficients, applied to the decomposed original image.

11. The improvement of claim 10, wherein said means for filtering comprises:

means for decomposing the original image by means of a wavelet transformation into plural wavelet scales; and

means for reconstructing the decomposed original image, including,

means for applying said three or more non-zero wavelet scale weighting coefficients to respective of the plural wavelet scales of the decomposed original image, and

means for performing a weighted inverse wavelet transformation utilizing the plural wavelet scales of the decomposed original image.

12. The improvement according to claim 9, wherein said means for selecting second candidate comprises:

means for applying Powell'"'"'s conjugate gradient to said first error and said first candidate weighting coefficients to determine said second candidate weighting coefficients.