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

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

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

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**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 Lets 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 Lets 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 dont 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 dont 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 Contd

**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