Compressive Sensing Techniques for Video Acquisition EE5359 Multimedia Processing December 8 2009 Madhu P Krishnan Contents Introduction to Image Acquisition Problem Statement Compressive Sensing Concept System Results Conclusion References 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 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 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 Concept Let x x 1 x N 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 M N measurement matrix independent identically distributed i i d Gaussian matrix The above expression can be written in terms of s as Concept Unfortunately reconstruction of x x 1 x N or equivalently s s 1 s N from vector y of M samples is not unique However excellent approximation can be obtained via the l1 norm minimization given by System Fig 3 Block diagram of the acquisition process 8 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 Results Fig 4 Sparsity determination Here C 4 and Th 100 are chosen as values to determine sparsity Results Fig 5 Sparsity determination Here C 4 and Th 400 are chosen as values to determine sparsity 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 Percentage of pels PSNR dB sampled PSNR dB 20 49 2290 27 8740 60 55 5468 32 0448 Tab 1 Percentage samples vs PSNR dB for Akiyo and Stefan 80 58 2653 38 3529 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 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 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 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 References 1 R G Baraniuk Compressive Sensing Lecture Notes in IEEE Signal Processing Magazine Vol 24 pp 118 120 July 2007 2 E Cand s J Romberg and T Tao Robust uncertainty principles Exact signal reconstruction from highly incomplete frequency information IEEE Trans Inform Theory vol 52 pp 489 509 Feb 2006 3 D Donoho Compressed sensing IEEE Trans Inform Theory vol 52 pp 1289 1306 Apr 2006 4 E Cand s 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 2435 2476 Oct 1998 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
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