MacSeNet/SpaRTan Spring School on Sparse Representations and - PowerPoint PPT Presentation

MacSeNet/SpaRTan Spring School on Sparse Representations and Compressed Sensing Sp Spar arse se R Rep eprese esenta ntati tion ons s an and d Di Diction ctionar ary y Le Lear arning ning for or So Sour urce ce Se Sepa parati tion on, , Lo Loca cali lisa sati tion on, , an and T d Trac acking king Wenwu Wang Reader in Signal Processing Centre for Vision, Speech and Signal Processing Department of Electronic Engineering University of Surrey, Guildford w. w.wang@surrey.ac.uk htt http://personal.ee.surrey.ac.uk/Personal/W /W.Wang/ 07 07/0 /04/2016 1

Contents o Dictionary Learning Sparse synthesis model (SimCO algorithm) o Sparse analysis model (Analysis SimCO o algorithm) o Application Examples • Source separation • Signal denoising & despeckling • Beamforming • Multi-speaker tracking o Future Work 2

Sparse Synth thesis Model ---- dictionary ---- signal ---- representation 3

Synthesis Spars rse Coding • Task: • Existing algorithms: (1) Greedy algorithms: OMP, SP (2) Relaxation algorithms: BP Y. Pati, R. Rezaiifar, and P. Krishnaprasad, “Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition,” in Proc. 27th Asilomar Conf. Signals, Syst. and Comput., pp. 40-44, 1993. W. Dai and O. Milenkovic, “Subspace pursuit for compressive sensing signal reconstruction,” IEEE Trans. Inf. Theory , vol. 55, pp. 2230-2249, 2009. S. Chen and D. Donoho, “Basis pursuit,” in Proc. 28th Asilomar Conf. Signals, Syst. and Comput ., vol. 1, pp. 41-44, 1994. 4

Synthesis Dic icti tionary Learning (SDL) • Task: • Existing algorithms: MOD, K-SVD, SimCO K. Engan, S. Aase, and J. Hakon Husoy, “Method of optimal directions for frame design,” in IEEE Int. Conf. on Acoust., Speech, and Signal Processing (ICASSP) , vol. 5, pp. 2443-2446, 1999. M. Aharon, m. Elad, and A. Bruckstein, “K -SVD: An algorithm for designing overcomplete dictionaries for sparse representations,” IEEE Trans. Signal Process ., vol. 54, no. 11, pp. 4311-4322, 2006. 5

Sim imCO – fo for r synth thesis is dic icti tionary le learnin ing fixed sparsity pattern - sparsity pattern (indices of all the non-zeros in X ) W. Dai, T. Xu , and W. Wang, “Simultaneous codeword optimization ( SimCO) for dictionary update 6 and learning,” IEEE Trans. Signal Process ., vol. 60, no. 12, pp. 6340-6353, 2012.

Sparse Analy lysis Model ---- analysis dictionary ---- signal ---- representation ---- cosparsity 7

Analysis is Pursuit • Task: Recover a signal 𝐳 belonging to the analysis model from its measurements • Existing algorithms: BG, OBG; GAP R. Rubinstein, T. Peleg, and M. Elad , “Analysis K -SVD: A dictionary- learning algorithm for the analysis sparse model,” IEEE Trans. Signal Process ., vol. 61, no. 3, pp. 661-677, 2013. S. Nam, M. E. Davies, M. Elad, and R. Gribonval , “The cosparse analysis model and algorithms,” Appl. Comput. Harm. Anal. , vol. 34, no. 1, pp. 30-56, 2013. 8

Analysis is Dic ictio ionary Learnin ing (ADL) • Task: 9

Analysis is Dic ictio ionary Learnin ing (ADL) • Existing algorithms: (1) Analysis K-SVD: high computational complexity (2) AOL: exclude the feasible dictionaries outside UNTF (3) LOST: less effective in reaching the pre-defined cosparsity R. Rubinstein, T. Peleg, and M. Elad , “Analysis K -SVD: A dictionary- learning algorithm for the analysis sparse model,” IEEE Trans. Signal Process., vol. 61, no. 3, pp. 661-677, 2013. M. Yaghoobi, S. Nam, R. Gribonval , and M. Davies, “Constrained overcomplete analysis operator learning for cosparse signal modelling ,” IEEE Trans. Signal Process., vol. 61, no. 9, pp. 2341-2355, 2013. S. Ravishankar and Y. Bresler , “Learning overcomplete sparsifying transforms for siangl processing,” in IEEE Int. Conf. on Acoust., Speech, and Signal Processing (ICASSP) , pp. 3088-3092, 2013. 10

Analysis is Sim imCO Alg lgorit ithm • cost function: W. Dai, T. Xu , and W. Wang, “Simultaneous codeword optimisation ( SimCO) for dictionary update and learning", IEEE Transactions on Signal Processing , vol. 60, no. 12, pp. 6340-6353, 2012. 11

Analysis is Sim imCO fr framework 12

Analysis is Sim imCO – Dic ictionary Update J. Dong, W. Wang, W. Dai, M. Plumbley, Z. Han, and J. A. Chambers, "Analysis SimCO algorithms for sparse analysis model based dictionary learning", IEEE Transactions on Signal Processing , vol. 64, no. 2, pp. 417 - 431, 13 2016.

Imple Im lementation o Matlab toolbox of dictionary learning algorithms: SimCO • The toolbox contains implementation of multiple dictionary learning algorithms including our own algorithms primitive SimCO and regularised SimCO algorithms, as well as baseline algorithms including K-SVD, and MOD. • The toolbox has been made publicly available in compliance with EPSRC open access policy. Web address: http://personal.ee.surrey.ac.uk/Personal/W.Wang/codes/Si mCO.html 14

Imple Im lementation (cont.) o Matlab toolbox of analysis dictionary learning algorithms: Analysis SimCO • The toolbox contains implementation of multiple dictionary learning algorithms including our own algorithms Analysis SimCO, Incoherent Analysis SimCO algorithms, as well as several baseline algorithms including Analysis K-SVD, LOST, GOAL, AOL, TK-SVD. • The toolbox has been made publicly available in compliance with EPSRC open access policy. Web address: http://dx.doi.org/10.15126/surreydata.00808101 15

Pote tenti tial l Appli lications • Compressed Sensing • Image denoising • Image compression • Blind Source Separation • Inpainting • Recognition • Beamforming ……. 16

Sele lected Examples o Signal denoising o Source separation o Beamforming o Multi-speaker tracking 17

Denoising Examples Test images W. Dai, T. Xu , and W. Wang, “Simultaneous codeword optimization ( SimCO) for dictionary update 18 and learning,” IEEE Trans. Signal Process ., vol. 60, no. 12, pp. 6340-6353, 2012.

Natural Im Image Denois ising Test images Training images 19

PSNR Results (Input PSNR ~ 15 dB) J. Dong, W. Wang, W. Dai, M. Plumbley, Z. Han, and J. A. Chambers, "Analysis SimCO algorithms for sparse analysis model based dictionary learning", IEEE Transactions on Signal Processing , vol. 64, no. 2, pp. 417 - 431, 20 2016.

Despeckli ling – Sig ignal l Model Signal model: Transformed model: Optimisation problem: 21

Despeckli ling – Sig ignal l Recovery Alternating direction method of multipliers (ADMM): Augumented Lagrangian function of the above function: 22

Despeckli ling – Real l SAR Im Images J. Dong, W. Wang, J. A. Chambers, "Removing speckle noise by analysis dictionary learning", in Proc. IEEE Sensor Signal Processing for Defence (SSPD 2015), Edinburgh, UK, September 9-10, 2015. 23

Source Separatio ion: Cocktail l part rty pro roblem Microphone1 x 1 t ( ) Speaker1 s 1 t ( ) x 2 t ( ) Microphone2 s 2 t ( ) Speaker2 24

Bli lind Source Separation & In Independent Component Analysis is Mixing Process Unmixing Process s 1 x 1 Y 1 H W s x M Y N Independent? N Unknown Known Optimize x  Hs Mixing Model: Diagonal Scaling Matrix    y Wx WHs PDs De-mixing Model: Permutation Matrix 25

Fre requency Domain BSS & Permutation Pro roblem S 1 × 0.5  S 1 x 1 1 ˆ S 2 × 1 1  S ( ) S 2 × 0.6  2 S 1 × 0.4 S 2 × 0.3 ˆ  2  S ( ) S 2 x 2 P S 1 × 1.2 FDICA Solutions: • Beamforming • Spectral envelope correlation 26

Computati tional Audit itory Scene Analysis is • Computational models for two conceptual processes of auditory scene analysis (ASA): – Segmentation . Decompose the acoustic mixture into sensory elements (segments) – Grouping . Combine segments into groups, so that segments in the same group likely originate from the same sound source 27

CASA – Tim ime-Frequency Masking Demos due to Deliang Wang. Recent psychophysical tests show that the ideal binary mask results in dramatic speech intelligibility improvements (Brungart et al.’06; Li & Loizou’08) 28

Underdetermined Source Separation Time-frequency domain Time domain s   x  1      a a a a  11 12 13 14   1          x a a a a       s 2 21 22 23 24   4 29