Using an MM-principle to enforce a sparsity constraint on fast image data estimation from large image data sets

• US 9,864,046 B2
• Filed: 06/16/2014
• Issued: 01/09/2018
• Est. Priority Date: 06/15/2013
• Status: Active Grant

• Current Assignee: Howard University
• Original Assignee: Howard University
• Inventors: Anderson, John M. M., Ndoye, Mandoye, Ode, Oludotun, Ogworonjo, Henry C.
• Primary Examiner(s): Bythrow, Peter
• Assistant Examiner(s): Malley, Sr., Daniel P
• Application Number:
  US14/305,934
• Publication Number:
  US 20160202346A1
• Time in Patent Office: 1,303 Days
• CPC Class Codes: G01S 13/0209 Systems with very large relative bandwidth, i.e. larger than 10 %, e.g. baseband, pulse, carrier-free, ultrawideband
• CPC Class Codes: G01S 13/885 for ground probing prospecting or detecting using electromagnetic waves G01V3/12
• CPC Class Codes: G01S 13/887 for detection of concealed objects, e.g. contraband or weapons
• CPC Class Codes: G01S 13/89 for mapping or imaging
• CPC Class Codes: G01S 7/292 Extracting wanted echo-signals
• CPC Class Codes: G01S 7/2923 based on data belonging to a number of consecutive radar periods
• CPC Class Codes: G06F 18/2415 based on parametric or probabilistic models, e.g. based on likelihood ratio or false acceptance rate versus a false rejection rate
• CPC Class Codes: G06V 20/56 exterior to a vehicle by using sensors mounted on the vehicle

Abstract

The mathematical majorize-minimize principle is applied in various ways to process the image data to provide a more reliable image from the backscatter data using a reduced amount of memory and processing resources. A processing device processes the data set by creating an estimated image value for each voxel in the image by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve a maximum a posteriori (MAP) estimation problem associated with a mathematical model of image data from the data. A prior probability density function for the unknown reflection coefficients is used to apply an assumption that a majority of the reflection coefficients are small. The described prior probability density functions promote sparse solutions automatically estimated from the observed data.

Claims

1. A method of creating an image from received data by estimating unknown reflection coefficients for individual voxels in a scene of interest (SOI), the method comprising:

receiving the data;

processing the data with a processing device by iteratively deriving an estimated image value for individual voxels in the image through application of a majorize-minimize technique to minimize a maximum a posteriori (MAP) objective function applied to the data, wherein the MAP objective function includes;

a data component including at least a portion of the data, and

a prior probability density function for the unknown reflection coefficients configured to apply a restriction that a majority of the reflection coefficients are equal to zero or substantially equal to zero;

displaying the image using the estimated image value of individual voxels of the scene of interest.

2. The method of claim 1 wherein the receiving the data comprises receiving data including information representing 1) transmission site locations of radar return signals, 2) reception site locations of reception of reflections from the radar pulses, 3) radar-return profiles for pairings of the transmission site locations and the reception site locations, and 4) data samples associated with individual radar-return profiles.

3. The method of claim 1 wherein the data component of the MAP objective function is

4. The method of claim 3 wherein the prior probability density function for the unknown reflection coefficients is

5. The method of claim 4 wherein the iteratively deriving the estimated image value comprises iteratively deriving the reflection coefficient for a given voxel using

for l=1,2, . . . , L

6. The method of claim 5 wherein

7. The method of claim 3 wherein a negative log of a summation of the prior probability density function for the unknown reflection coefficients is

8. The method of claim 7 wherein the iteratively deriving the estimated image value comprises iteratively deriving the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

9. The method of claim 8 wherein

10. The method of claim 3 wherein the prior probability density function for the unknown reflection coefficients is a function with an approximately uniform peak across a width, wherein beyond the width the function decays to zero.

11. The method of claim 10 wherein the function is defined as

12. The method of claim 11 wherein the iteratively deriving the estimated image value comprises iteratively deriving the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

13. The method of claim 12 wherein the variance of the noise in the data is estimated using a maximum likelihood estimate of noise power.

14. The method of claim 13 wherein the maximum likelihood estimate of noise power for iterate number (m) is given by

15. The method of claim 1 wherein the calculating the terms comprises:

computing G_l^(m) by applying a hash-table-based computation to

16. The method of claim 15 further comprising computing G_l^(m) via i=1,2, . . . , I;

j=1,2, . . . , J;

l=1,2, . . . , L

17. The method of claim 12 wherein the calculating of the terms comprises:

computing H_l by applying a hash-table-based computation to

|S_k|

where |S_k| denotes a number of elements in the set S_k.

18. The method of claim 17 wherein the computing H_l further comprises computing H_l via

i=1,2, . . . . ,I;

j=1,2, . . . . ,J;

l=1,2, . . . ,L

19. The method of claim 1 further comprising:

emitting a radar pulse at specified intervals into a scene of interest;

detecting amplitudes of signal reflections from the scene of interest from the radar pulse;

recording position data corresponding to individual radar pulse emissions and individual receptions of the signal reflections; and

creating the initial data set from the position data and detected amplitudes of the signal reflections.

37. The method of claim 3 wherein the prior probability density function for the unknown reflection coefficients is

38. The method of claim 37 wherein the iteratively deriving the estimated image value comprises iteratively deriving the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

39. The method of claim 3 wherein a negative log of a summation of the prior probability density function for the unknown reflection coefficients is

40. The method of claim 39 wherein the iteratively deriving the estimated image value comprises iteratively deriving the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

20. An apparatus for detecting objects in a scene of interest, the apparatus comprising:

a vehicle;

a plurality of radar transmission devices mounted on the vehicle and configured to transmit radar pulses into a scene of interest;

a plurality of radar reception devices mounted on the vehicle, individual ones of the plurality of radar reception devices being configured to detect amplitudes of signal reflections received from the scene of interest from the radar pulses;

a location determination device configured to detect a location of the vehicle at a time of transmission of the radar pulse from the plurality of radar transmission devices and reception of the signal reflections by the radar reception devices;

a processing device configured to process a data set including information representing

     1) transmission site locations of individual ones of the radar pulses,

     2)reception site locations of reception of individual ones of the signal reflections, and

     3) a number of data samples per reception profile by;

iteratively deriving an estimated image value for each voxel in the image through application of a majorize-minimize technique to minimize a maximum a posteriori (MAP) objective function applied to the data wherein the MAP objective function includes;

a data component including at least a portion of the data, and

a prior probability density function for the unknown reflection coefficients to apply an assumption that a majority of the reflection coefficients are equal to zero or substantially equal to zero.

21. The apparatus of claim 20 wherein the processing device is further configured to calculate the data component of the MAP objective function as

22. The apparatus of claim 21 wherein the processing device is further configured to use the prior probability density function for the unknown reflection coefficients defined as

23. The apparatus of claim 22 wherein the processing device is further configured to iteratively derive the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

24. The apparatus of claim 23 wherein

25. The apparatus of claim 21 wherein the processing device is further configured to use a negative log of a summation of the prior probability density function for the unknown reflection coefficients as

26. The apparatus of claim 25 wherein the processing device is further configured to iteratively derive the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

27. The apparatus of claim 26 wherein

28. The apparatus of claim 21 wherein the prior probability density function for the unknown reflection coefficients is a function with an approximately uniform peak across a width, wherein beyond the width the function decays to zero.

29. The apparatus of claim 28 wherein the function is defined as

30. The apparatus of claim 29 wherein the processing device is further configured to iteratively derive the estimated image value comprises iteratively deriving the reflection coefficient for a given voxel using

f or l=1,2, . . . , L

31. The apparatus of claim 30 wherein the variance of the noise in the data is estimated using a maximum likelihood estimate of noise power.

32. The apparatus of claim 31 wherein the maximum likelihood estimate of noise power for the iterate number (m) is given by

33. The apparatus of claim 20 wherein the processing device is configured to calculate the terms by:

computing G_l^(m) by applying a hash-table-based computation to

34. The apparatus of claim 33 wherein the processing device is further configured to compute G_l^(m) via

i=1, 2, . . . , I;

j=1, 2, . . . , J;

l=1, 2, . . . , L

35. The apparatus of claim 20 wherein processing device is configured to calculate the terms by:

computing H_l by applying a hash-table-based computation to

|S_k|

where |S_k| denotes a number of elements in the set S_k.

36. The apparatus of claim 35 wherein the processing device is configured to compute H_l via

i=1, 2, . . . . , l;

j=1, 2, . . . . , J;

l=1, 2, . . . , L

41. The apparatus of claim 21 wherein the processing device is further configured to use a negative log of a summation of the prior probability density function for the unknown reflection coefficients as

42. The apparatus of claim 41 wherein the processing device is further configured to iteratively derive the reflection coefficient for a given voxel using

f or l=1, 2, . . . , L

43. The apparatus of claim 21 wherein the processing device is further configured to use a negative log of a summation of the prior probability density function for the unknown reflection coefficients as

44. The apparatus of claim 43 wherein the processing device is further configured to iteratively derive the reflection coefficient for a given voxel using

f or l=1, 2, . . . , L