Change Detection An Invitation for Applying MIMO Compressive Sensing in Through Wall Radar Imaging Moeness Amin Vill

1. Change Detection � An Invitation for Applying MIMO & Compressive Sensing in Through Wall Radar ImagingMoeness AminVillanova University, USABarcelona-Spain 7-2010

3. Imaging of Building Interiors and Personnel

4. Detecting Weapon Caches

6. Detection of Human and Human Gait Classifications

9. Motion Detection and Classifications

10. Scene- Without Target

11. Scene-Without Target

12. Scene with Target

13. Experiment I

14. Signal Processing

15. Signal Processing Method

16. Results with CFAR

17. Subtractions from a Reference Position

18. Two Crossing Targets III

19. Two Moving Targets

20. CFAR CD

21. Observations With Change Detection The image is sparse The target is a Human Target localization is the goal

22. Other Strategies 22

24. Compressed Sensing (CS) CS is to find sparse solution from under-determined linear system (J < D) It is done by l1 norm minimization such that CS is very efficient reconstruction technique Reconstruction with very few data samples Compressed sensing, which is one of the most active research field these days, is proposed to significantly reduce the number of data sample for signal reconstruction. It can find sparse solution from under-determined linear system. Consider a J dimensional vector y. When D, which is the dimension of vector s, is larger than J, it is usually impossible to uniquely find s from y. However, when s is a sparse vector, it is possible to reconstruct s from y. When the matrix phi and psi satisfies some properties. Compressed sensing, which is one of the most active research field these days, is proposed to significantly reduce the number of data sample for signal reconstruction. It can find sparse solution from under-determined linear system. Consider a J dimensional vector y. When D, which is the dimension of vector s, is larger than J, it is usually impossible to uniquely find s from y. However, when s is a sparse vector, it is possible to reconstruct s from y. When the matrix phi and psi satisfies some properties.

25. CS in Radar Imaging Let s[k,l], for k=0,�,K-1 and l=0,�,L-1, be the spatially sampled scene of interest, s(x,y) Let M be the number of antenna positions Let N be the number of frequencies in the stepped-frequency signal Let s of k l be the spatially sampled scene of interest. Let M and N be the number of antenna positions and the number of frequencies. So, y[m,n] is M by N data matrix and s[k,l] is K by L signal matrix to be reconstructedLet s of k l be the spatially sampled scene of interest. Let M and N be the number of antenna positions and the number of frequencies. So, y[m,n] is M by N data matrix and s[k,l] is K by L signal matrix to be reconstructed

26. CS in Radar Imaging We can rewrite the received signal y into a matrix-vector form  ? is a MN ? KL matrix such as Let�s convert the signal matrix and the scene matrix into long vector by stacking all column. Then, the received signal vector can be represented by a psi matrix multiplied by the scene vector s. Here the psi matrix is nothing but two-dimensional Fourier transform matrix such that Let�s convert the signal matrix and the scene matrix into long vector by stacking all column. Then, the received signal vector can be represented by a psi matrix multiplied by the scene vector s. Here the psi matrix is nothing but two-dimensional Fourier transform matrix such that

27. Measurement Matrix Let ? be a J ? KL measurement matrix that has only one nonzero element, which is one, at each row The indexes i0,�,iJ-1 are randomly chosen in [0,MN-1] Let phi be a J by KL measurement matrix that has only one nonzero element in each row. If we define y sub CS as a data set for CS such that it is just J selected samples out of KL possible data set. Now, we will try to reconstruct s from y cs which is J dimensional vector instead of y which is M time N dimensional vector.Let phi be a J by KL measurement matrix that has only one nonzero element in each row. If we define y sub CS as a data set for CS such that it is just J selected samples out of KL possible data set. Now, we will try to reconstruct s from y cs which is J dimensional vector instead of y which is M time N dimensional vector.

28. Reconstruction by l1 norm minimization Given ycs such that ycs is a J-dimensional vector ? ( > 0) gives robustness The reconstruction can be done by l1 norm minimization like this. Here, epsilon gives some robustness to the problem due to errors or noise in the data set. All the vectors are complex numbers and it should be converted into real valued matrix before optimization. It can be easily done by separating real part and imaginary part of the data.The reconstruction can be done by l1 norm minimization like this. Here, epsilon gives some robustness to the problem due to errors or noise in the data set. All the vectors are complex numbers and it should be converted into real valued matrix before optimization. It can be easily done by separating real part and imaginary part of the data.

29. Measurement Matrix Data measurement comparison Conventional radar measures MN samples CS radar measures only J samples (samples are randomly chosen) If we use only J samples, we don�t need to collect all MN samples. The left figure represents data samples that is required for conventional high-resolution radar. It should transmit all M narrowband signals at all N locations. On the other hands, if it require only J samples, we can skip many locations and signals and the data collecting time will be significantly reduced. This is the advantage of compressed sensing.If we use only J samples, we don�t need to collect all MN samples. The left figure represents data samples that is required for conventional high-resolution radar. It should transmit all M narrowband signals at all N locations. On the other hands, if it require only J samples, we can skip many locations and signals and the data collecting time will be significantly reduced. This is the advantage of compressed sensing.

31. Sparse Constraint Optimization Data

33. Experimental Setup Stepped-frequency CW signal 201 frequency steps Step size: 10 MHz Bandwidth: 2 GHz centered at 2 GHz MIMO Radar System 21-element uniformly spaced receive line array of length 1.5m 2 Transmitters placed slightly above and on either side of the receive array Solid concrete block wall Thickness: 0.14m Standoff distance from the wall Receivers: 1.06m Transmitters: 1.34m

34. Scene Layout

35. Background Scene

36. Target Movements Person sways his torso backwards, forwards, to the right, and to the left Both large and small swaying movements were measured

37. Large Displacements

38. Small Displacements

39. Back Large

40. Back Small

41. Forward Large

42. Forward Small

43. Left Large

44. Left Small

45. Right Large

46. Right Small

47. Compressive Sensing �Taking Advantage of Target RCS Signatures

59. MIMO-MTI Approach for TWRI Applications

60. MIMO Radar System MIMO Radar System Synthetic uniform line array of receivers with an inter-element spacing of 7.49cm 2 Transmitters placed (slightly above and slightly behind) on either side of the receive array Virtual Array or Co-Array The diagram shows a top down view of arrays and coarrays. Black dots are the receivers. Gray dots are the Transmitters and Blue dots represent the coarray. In case of SIMO, only one transmitter will be activated, Thus the corresponding coarray will be the same as the length of the receive arrayThe diagram shows a top down view of arrays and coarrays. Black dots are the receivers. Gray dots are the Transmitters and Blue dots represent the coarray. In case of SIMO, only one transmitter will be activated, Thus the corresponding coarray will be the same as the length of the receive array

62. Experimental Setup Stepped-frequency CW signal 201 frequency steps Step size: 10 MHz Bandwidth: 2 GHz centered at 2 GHz MIMO Radar System 21-element uniformly spaced receive line array of length 1.5m 2 Transmitters placed slightly above and on either side of the receive array Solid concrete block wall Thickness: 0.14m Standoff distance from the wall Receivers: 1.06m Transmitters: 1.34m

63. Scene Layout

64. Background Populated Scene

65. Target Movements Measurements were made with the targets at the following ten positions Position 1 is closest to the wall and position 10 is farthestPosition 1 is closest to the wall and position 10 is farthest

66. Target Movements � Cont�d

67. Images before Change Detection MIMO Radar was usedMIMO Radar was used

68. Change Detection Results

70. Experimental Setup Stepped-frequency CW signal 201 frequency steps Step size: 10 MHz Bandwidth: 2 GHz centered at 2 GHz MIMO Radar System 15-element uniformly spaced receive line array of length 1.0m 2 Transmitters placed slightly above and on either side of the receive array Solid concrete block wall Thickness: 0.14m Standoff distance from the wall Receivers: 1.06m Transmitters: 1.34m

71. Scene Layout

72. Target Movements

73. Change Detection Results Total of six positions were measured. Position 1 is farthest from the wall and Position 6 is closest to the wallTotal of six positions were measured. Position 1 is farthest from the wall and Position 6 is closest to the wall

74. Conclusions Through wall radar imaging is a fertile area for emerging techniques in signal analyses and processing