Distributed Compressive Video Sensing

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Distributed Compressive Video Sensing
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Distributed Source Coding
Slepian and Wolf, 1973
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Distributed Video Coding
Wyner-ZivIntraframe Encoder
Wyner-ZivInterframe Decoder
X
X
Girod, 2006
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Distributed Video Coding

• The statistical dependency between X and Y
• Laplacian distribution

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Compressive Sensing

• When data is sparse/compressible, one can
  directly acquire a condensed representation with
  no/little information loss
• Random projection will work

Baraniuk, 2008
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Compressive Sensing

• Directly acquire compressed data
• Replace samples by more general measurements

Baraniuk, 2008
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Compressive Sensing

• y ?x ??? A?

x ??
y
?
?
?
M1
MN
N1
NN
A ??
Baraniuk, 2008
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Measurement Matrix

• Scrambled block Hadamard ensemble (SBHE)
• partial block hadamard transform and random
  column permutation
• ? QMWPN
• L. Gan, T. T. Do, and T. D. Tran, Fast
  compressive imaging using scrambled hadamard
  ensemble, in Proc. of European Signal Processing
  Conf., Lausanne, Switzerland, August 2008
  (EUSIPCO2008).

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Signal Reconstruction

• The convex unconstrained optimization problem
• Can be seen as a maximum a posteriori criterion
  for estimating ? from
• y A ? n,
• where n is white Gaussian noise

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Signal Reconstruction

• Signal recovery from random measurements
• Gradient projection for sparse reconstruction
  (GPSR)
• Two-step iterative shrinkage/thresholding
  algorithm (TwIST)
• Orthogonal matching pursuit (OMP)
• M. A. T. Figueiredo, R. D. Nowak, and S. J.
  Wright, Gradient projection for sparse
  reconstruction application to compressed sensing
  and other inverse problems, IEEE J. of Selected
  Topics in Signal Processing, vol. 1,no. 4, pp.
  586-597, Dec. 2007.
• J. M. Bioucas-Dias and M. A. T. Figueiredo,
  A new TwIST two-step iterative
  shrinkage/thresholding algorithms for image
  restoration, IEEE Trans. on Image Processing,
  vol. 16, no. 12, pp. 2992-3004, Dec. 2007.
• T. Blumensath and M. E. Davies, Gradient
  pursuits, IEEE Trans. on Signal Processing, vol.
  56, June 2008.

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Distributed Compressive Video Sensing

• Measurement matrix ? scrambled block Hadamard
  ensemble (SBHE)
• Sparse basis matrix ? DWT
• Video signal sensing (encoder) general random
  projection
• Video signal recovery (decoder)
• Key frame GPSR with default settings
• CS frame
• side information generation (motion compensated
  interpolation)
• GPSR with the proposed initialization and the
  proposed termination criteria

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Distributed Compressive Video Sensing
Compressive video sensing
Video signal recovery
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Distributed Compressive Video Sensing

• At the decoder, for a CS frame xt ??t
• its side information St ??St can be generated
  from its previous reconstructed key frames
• Proposed initialization
• initial solution at the 0-th iteration
  
• a(xt, St) the Laplacian parameter of (xt- St)

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Side information generation
yt-1 Fxt-1 with higher MR
GPSR reconstruction
Reconstructed frame (t-1)
Key frame (t - 1)
Proposed Modified GPSR reconstruction
yt Fxt with lower MR
Non-key frame t
Side information (t)
Reconstructed frame (t)
yt1 Fxt1 with higher MR
GPSR reconstruction
Key frame (t 1)
Reconstructed frame (t1)
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Distributed Compressive Video Sensing
a(xt, )
a( , St)
xt
St
a(xt, St)
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Proposed Termination Criterion

• First
• Second
• Third

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Proposed Termination Criterion

• MR is low (MR 20) if the First criterion with
  Ta 0.9 is satisfied, the algorithm will stop
• MR is middle (20 lt MR 70) if the First
  criterion with Ta 0.05 or the Second criterion
  is satisfied, the algorithm will stop
• MR is high (MR gt 70) if the Third criterion
  with TF 0.001 is satisfied, the algorithm will
  stop

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Simulation Results

• Foreman and Coastguard CIF video sequences with
  300 Y frames (352288 101376 samples for each Y
  frame) and GOP size 3 (Key, Non-key, Non-key,
  Key, )
• The three approaches for comparison (all with
  default settings)
• GPSR, TwIST, OMP
• For OMP, block size 3232 suggested by
• V. Stankovic, L. Stankovic, and S. Cheng,
  Compressive video sampling, in Proc. of
  European Signal Processing Conf., Lausanne,
  Switzerland, August 2008 (EUSIPCO2008).

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Simulation Results
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Simulation Results
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Simulation Results
The reconstruction complexities for the Foreman
sequence
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Simulation Results
The PSNR performance at different reconstruction
complexities for the Foreman sequence
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Simulation Results
(a) Side information
(b) Reconstructed frame
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Simulation Results
The reconstructed Foreman sequences (352288 for
each frame) at measurement rate (MR) 0.3 using
(a) GPSR (gradient projection for sparse
reconstruction) (average PSNR 27.68 dB)
(average reconstruction time 15.14 seconds per
frame) and (b) our DCVS (average PSNR 29.48
dB) (average reconstruction time 3.68 seconds
per frame) (This example shows the 54-th frame).
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Conclusions

• The proposed DCVS approach exploits the two
  characteristics
• distributed video coding (DVC)
• compressive sensing (CS)
• The proposed DCVS can outperform or be comparable
  with the three existing approaches for
  comparison, especially at lower measurement rates
• The proposed DCVS can significant outperform the
  three existing approaches at the same
  reconstruction complexity