Using an MM-principle to achieve fast image data estimation from large image data sets

• US 9,870,641 B2
• Filed: 02/19/2014
• Issued: 01/16/2018
• Est. Priority Date: 02/19/2013
• Status: Active Grant

• Current Assignee: Howard University
• Original Assignee: Howard University
• Inventors: Anderson, John M. M., Ndoye, Mandoye
• Primary Examiner(s): Nguyen, Phu K
• Application Number:
  US14/184,446
• Publication Number:
  US 20150279082A1
• Time in Patent Office: 1,427 Days
• Field of Search: 345419, 345424
• CPC Class Codes: G01S 13/003 Bistatic radar systems; Multistatic radar systems
• CPC Class Codes: G01S 13/885 for ground probing prospecting or detecting using electromagnetic waves G01V3/12
• CPC Class Codes: G01S 13/90 using synthetic aperture techniques , e.g. synthetic aperture radar [SAR] techniques
• CPC Class Codes: G01S 7/046 using an intermediate storage device, e.g. a recording/reproducing device
• CPC Class Codes: G01S 7/295 Means for transforming co-ordinates or for evaluating data, e.g. using computers
• CPC Class Codes: G06T 15/08 Volume rendering

Abstract

A majorize-minimize (MM) mathematical principle is applied to least squares regularization estimation problems to effect efficient processing of image data sets to provide good quality images. In a ground penetrating radar application, these approaches can reduce processing time and memory use by accounting for a symmetric nature of a given radar pulse, accounting for similar discrete time delays between transmission of a given radar pulse and reception of reflections from the given radar pulse, and accounting for a short duration of the given radar pulse.

Claims

1. A method of creating an image from an initial data set, the method comprising:

receiving the initial data set, the receiving comprising receiving data representing transmission site locations of radar pulses applied into ground in a ground penetrating radar application, reception site locations of reception of reflections from the radar pulses, radar-return profiles for pairings of the transmission site locations and the reception site locations, and data samples associated with individual radar-return profiles;

processing the initial data set with a processing device by creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set'"'"'s values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve an l₁-regularized least-squares estimation problem associated with a mathematical model of image data from the initial data set;

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

2. The method of claim 1 further comprising iteratively deriving an estimated image value for a given voxel using

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

3. The method of claim 1 further comprising calculating terms used to obtain the estimated image value,

wherein the calculating reduces processing time and required memory by accounting for a symmetric nature of a given radar pulse, accounting for similar discrete time delays between transmission of a given radar pulse and reception of reflections from the given radar pulse, and accounting for a short duration of the given radar pulse.

4. The method of claim 3 wherein the calculating the terms comprises:

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

5. The method of claim 4 further comprising computing G_l^(m) via

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

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

l=1,2, . . . ,L

6. The method of claim 3 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.

7. The method of claim 6 wherein the computing H_l further comprises computing H_l via

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

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

l=1,2, . . . ,L

8. The method of claim 1 further comprising:

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

detecting magnitude 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 magnitudes of the signal reflections.

9. A method of creating an image from an initial data set, the method comprising:

receiving the initial data set, the receiving comprising receiving data representing transmission site locations of radar pulses applied into ground in a ground penetrating radar application, reception site locations of reception of reflections from the radar pulses, radar-return profiles for pairings of the transmission site locations and the reception site locations, and data samples associated with individual radar-return profiles;

processing the initial data set with a processing device by;

creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set'"'"'s values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve the l₁-regularized least-absolute deviation estimation problem associated with a mathematical model of image data from the initial data set;

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

10. The method of claim 9 further comprising iteratively deriving an estimated image value for a given voxel using

11. The method of claim 9 further comprising calculating terms used to obtain the estimated image value,

wherein the calculating the terms reduces processing time and required memory by accounting for a symmetric nature of a given radar pulse, accounting for similar discrete time delays between transmission of a given radar pulse and reception of reflections from the given radar pulse, and accounting for a short duration of the given radar pulse.

12. The method of claim 11 wherein the calculating the terms comprises:

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

13. The method of claim 12 wherein the computing the term N_l^(m) further comprises computing N_l^(m) via

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

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

l=1,2, . . . ,L;

14. The method of claim 11 wherein the calculating the terms comprises:

computing D_l^(m) by applying a hash-table-based computation to |S_k| where |S_k| denotes a number of elements in the set S_k.

15. The method of claim 14 wherein the computing the term D_l^(m) further comprises computing D_l^(m) via

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

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

l=1,2, . . . ,L

16. The method of claim 9 further comprising:

emitting a radar pulse applied into ground in a ground penetrating radar application at specified intervals into a scene of interest;

detecting magnitude of signal reflections from the scene of interest from the radar pulse; and

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

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

17. 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 ground in a scene of interest;

a plurality of radar reception devices mounted on the vehicle configured to detect magnitude of signal reflections from the scene of interest from the radar pulses;

a location determination device configured to detect location of the vehicle at times 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 an initial data set representing transmission site locations of individual ones of the radar pulses, reception site locations of reception of individual ones of the signal reflections, and number of data samples per reception profile by;

creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set'"'"'s values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve an l₁-regularized least-squares estimation problem associated with a mathematical model of image data from the initial data set.

18. The apparatus of claim 17 wherein the processing device is further configured to iteratively derive an estimated image value for a given voxel using

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

19. The apparatus of claim 17 wherein the processing device is further configured to calculate terms used to obtain the estimated image value,

wherein the calculating reduces processing time and required memory by accounting for a symmetric nature of a given radar pulse, accounting for similar discrete time delays between transmission of a given radar pulse and reception of reflections from the given radar pulse, and accounting for a short duration of the given radar pulse.

20. The apparatus of claim 19 wherein the processing device is further configured to calculate terms by computing G_l^(m) by applying a hash-table-based computation to

21. The apparatus of claim 20 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

22. The apparatus of claim 19 wherein the processing device is further configured to calculate 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.

23. The apparatus of claim 22 wherein the processing device is further configured to compute H_l by computing H_l via

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

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

l=1,2, . . . ,L

24. 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 ground in a scene of interest;

a plurality of radar reception devices mounted on the vehicle configured to detect magnitude of signal reflections from the scene of interest from the radar pulses;

a location determination device configured to detect location of the vehicle at times 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 an initial data set representing transmission site locations of individual ones of the radar pulses, reception site locations of reception of individual ones of the signal reflections, and number of data samples per reception profile by;

creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set'"'"'s values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve the l₁-regularized least-absolute deviation estimation problem associated with a mathematical model of image data from the initial data set.

25. The apparatus of claim 24 wherein the processing device is further configured to iteratively derive an estimated image value for a given voxel using

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

26. The apparatus of claim 24 wherein the processing device is further configured to calculate terms used to obtain the estimated image value,

wherein the calculating the terms reduces processing time and required memory by accounting for a symmetric nature of a given radar pulse, accounting for similar discrete time delays between transmission of a given radar pulse and reception of reflections from the given radar pulse, and accounting for a short duration of the given radar pulse.

27. The apparatus of claim 26 wherein the processing device is further configured to calculate terms by computing N_l^(m) by applying a hash-table-based computation to

28. The apparatus of claim 27 wherein the processing device is further configured to compute N_l^(m) via

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

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

l=1,2, . . . ,L;

29. The apparatus of claim 26 wherein the processing device is further configured to calculate terms by computing D_l^(m) by applying a hash-table-based computation to |S_k| where |S_k| denotes a number of elements in the set S_k.

30. The apparatus of claim 29 wherein the processing device is further configured to calculate terms by computing D_l^(m) via

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

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

l=1,2, . . . ,L

31. A method of creating an image from a data set, the method comprising:

receiving a DAS image data set created by applying a delay-and-sum (DAS) algorithm to create an initial data set, the receiving comprising receiving data representing transmission site locations of radar pulses applied into ground in a ground penetrating radar application, reception site locations of reception of reflections from the radar pulses, radar-return profiles for pairings of the transmission site locations and the reception site locations, and data samples associated with individual radar-return profiles;

processing the DAS image data set with a processing device by creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set'"'"'s values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve an l₁-regularized least-squares estimation problem that selects a sparse image derived from the DAS image data set;

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

32. The method of claim 31 further comprising iteratively deriving an estimated image value for a given voxel using

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

33. The method of claim 31 further comprising:

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

detecting magnitude 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;

creating the initial data set from the position data and detected magnitudes of the signal reflections; and

applying the delay-and-sum (DAS) algorithm to the initial data set to create the DAS image data set.

34. 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 ground in a scene of interest;

a plurality of radar reception devices mounted on the vehicle configured to detect magnitude of signal reflections from the scene of interest from the radar pulses;

a location determination device configured to detect location of the vehicle at times 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 an initial data set representing transmission site locations of individual ones of the radar pulses, reception site locations of reception of individual ones of the signal reflections, and number of data samples per reception profile by;

applying a delay-and-sum (DAS) algorithm to the initial data set to create a DAS image data set,

creating an estimated image value for each voxel in the image to create an estimated image value data set having most of the estimated image value data set'"'"'s values at or near zero by iteratively deriving the estimated image value through application of a majorize-minimize principle to solve an l₁-regularized least-squares estimation problem that selects a sparse image derived from the DAS image data set.

35. The apparatus of claim 34 wherein the processing device is further configured to iteratively derive an estimated image value for a given voxel using

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