Compressive Sensing Techniques for Video Acquisition

1
Compressive Sensing Techniques for Video
Acquisition

• EE5359 Multimedia Processing
• December 8,2009
• Madhu P. Krishnan

2
Contents

• Introduction to Image Acquisition
• Problem Statement
• Compressive Sensing
• Concept
• System
• Results
• Conclusion
• References

3
Introduction to Image Acquisition

• Long-established paradigm for Digital image
  acquisition
• Sample the complete image to get N pixel values
• Represent the sampled image in some transform
  domain
• Discard the non-significant coefficients(N K)
  in the transform domain.
• Transmit/store
• Fig.1
  Digital image acquisition system

4
Problem Statement

• Is it possible to create an efficient sensing
  process where we economize on the number of pixel
  measurements required and to reconstruct the
  scene, provided that we are not interested in the
  perfect reconstruction of the whole scene ?

5
Compressive Sensing

• A framework that enables sampling below Nyquist
  rate, with a small sacrifice in reconstruction
  quality.
• Compressive sampling shows us how image
  compression can be implicitly incorporated into
  the image acquisition process .
• Fig.2 Compressive
  sensing based data acquisition system

6
Concept

• Let x x1, . . . ,xN be a set of N pixels
  of an image. Let s be the representation of x
  in the transform domain, that is
• Let y be an M-length measurement vector given by
  , where is a MN measurement
  matrix(independent identically distributed
  (i.i.d.) Gaussian matrix). The above expression
  can be written in terms of s as

7
Concept

• Unfortunately, reconstruction of x x1, . . .
  ,xN (or equivalently, s s1, . . . ,
  sN) from vector y of M samples is not unique.
• However, excellent approximation can be obtained
  via the l1 norm minimization given by

8
System
Fig.3 Block diagram of the acquisition
process8.
9
Results

• The system described in Fig.3 is applied to
  Y-components of the QCIF Akiyo and CIF Stefan
  sequences.
• The sparse blocks are identified using DCT in the
  following manner. Let C be a small positive
  constant, and Th an integer threshold that is
  representative of the average number of
  significant DCT coefficients over all blocks. If
  the number of DCT coefficients in the block whose
  absolute value is larger than C is greater than
  Th, the block is selected as a reference for
  compressive sampling.
• Fig.4 and Fig.5 shows the number of DCT
  coefficients less than C for the first frame of
  Akiyo and Stefan sequence.

10
Results

• Fig.4 Sparsity determination (Here C 4 and
  Th 100 are chosen as values to determine
  sparsity).

11
Results

• Fig.5 Sparsity determination (Here C 4 and Th
  400 are chosen as values to determine sparsity).

12
Results

• The 9th frame of the Akiyo and 3rd frame of
  Stefan is compressively sampled, with their
  respective first frames used as reference. The
  results are shown as PSNR verses the percentage
  of the collected samples for a fixed Th.
• Tab.1 Percentage samples vs PSNR(dB)
  for Akiyo and Stefan

13
Results
Fig.6 9th frame reconstructed from 20 of pels
from selected blocks.
Fig.7 9th frame reconstructed from 40 of pels
from selected blocks.
14
Results

• Fig.8 9th frame reconstructed from 60 of pels
  from selected blocks

Fig.9 3rd frame reconstructed from 20 of pels
from selected blocks
15
Results

• Fig.10 3rd frame reconstructed from 40 of pels
  from selected blocks

Fig.11 3rd frame reconstructed from 60 of pels
from selected blocks
16
Conclusion

• 80 savings in acquisition can be achieved for
  video sequences like Akiyo, that are mostly
  static across frames , with good reconstruction
  quality.
• The results on Stefan sequence shows that for
  scenes with increased dynamics more pixels have
  to sampled(in this case 80) for good
  reconstruction quality.
• Simplification of the subsequent processing
  algorithms.

17
References

• 1 R. G. Baraniuk, "Compressive Sensing,
  Lecture Notes in IEEE Signal Processing Magazine,
  Vol. 24, pp. 118-120, July 2007.
• 2 E. Candès, J. Romberg, and T. Tao, Robust
  uncertainty principles Exact signal
  reconstruction from highly incomplete frequency
  information, IEEE Trans. Inform. Theory, vol.52,
  pp. 489509, Feb. 2006.
• 3 D. Donoho, Compressed sensing, IEEE Trans.
  Inform. Theory, vol. 52, pp. 1289-1306, Apr.
  2006.
• 4 E. Candès and M. Wakin, An introduction to
  compressive sampling, IEEE Signal Processing
  Magazine, vol. 25, pp. 21 - 30, March 2008.
• 5 D.L. Donoho et al. Data compression and
  harmonic analysis, IEEE Trans. Inform. Theory,
  vol. 44, pp. 24352476, Oct. 1998.

18
References

• 6 M. Vetterli and J. Kovacevic, Wavelets and
  Subband Coding. Englewood Cliffs, NJ
  Prentice-Hall, 1995.
• 7 J. Romberg, Imaging via compressive
  sampling, IEEE Signal Processing Magazine, vol.
  25, pp. 14 - 20, March 2008.
• 8 V. Stankovic, L. Stankovic, and S. Cheng,
  Compressive video sampling, Proc. Eusipco-2008
  16th European Signal Processing Conference,
  Lausanne, Switzerland, August 2008.
• 9 J. Tropp and A. C. Gilbert, Signal recovery
  from partial information via orthogonal matching
  pursuit, IEEE Trans. Info. Theory, vol. 53, pp.
  4655--4666, Dec. 2007.
• 10 N. Ahmed, T. Natarajan, and K. R. Rao,
  "Discrete Cosine Transform", IEEE Trans.
  Computers, Vol C-23, pp. 90-93, Jan 1974.