Learning multiscale sparse representations for image and video restoration

被引:311
作者
Mairal, Julien [2 ]
Sapiro, Guillermo [1 ]
Elad, Michael [3 ]
机构
[1] Univ Minnesota, Dept Elect & Comp Engn, Minneapolis, MN 55455 USA
[2] Ecole Normale Super, CNRS, WILLOW Project Team, UMR 8548,INRIA,ENS,Dept Informat, F-75230 Paris 05, France
[3] Technion Israel Inst Technol, Dept Comp Sci, IL-32000 Haifa, Israel
关键词
image and video processing; sparsity; dictionary; multiscale representation; denoising; inpainting; interpolation; learning;
D O I
10.1137/070697653
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper presents a framework for learning multiscale sparse representations of color images and video with overcomplete dictionaries. A single-scale K-SVD algorithm was introduced in [M. Aharon, M. Elad, and A. M. Bruckstein, IEEE Trans. Signal Process., 54 (2006), pp. 4311-4322], formulating sparse dictionary learning for grayscale image representation as an optimization problem, efficiently solved via orthogonal matching pursuit (OMP) and singular value decomposition (SVD). Following this work, we propose a multiscale learned representation, obtained by using an efficient quadtree decomposition of the learned dictionary and overlapping image patches. The proposed framework provides an alternative to predefined dictionaries such as wavelets and is shown to lead to state-of-the-art results in a number of image and video enhancement and restoration applications. This paper describes the proposed framework and accompanies it by numerous examples demonstrating its strength.
引用
收藏
页码:214 / 241
页数:28
相关论文
共 44 条
[1]   K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation [J].
Aharon, Michal ;
Elad, Michael ;
Bruckstein, Alfred .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2006, 54 (11) :4311-4322
[2]  
[Anonymous], 2007, ADV NEURAL INFORM PR
[3]  
[Anonymous], 1999, WAVELET TOUR SIGNAL
[4]  
[Anonymous], P SPIE ELECT IMAGING
[5]   Image inpainting [J].
Bertalmio, M ;
Sapiro, G ;
Caselles, V ;
Ballester, C .
SIGGRAPH 2000 CONFERENCE PROCEEDINGS, 2000, :417-424
[6]  
Bjorck A., 1996, NUMERICAL METHODS LE, DOI DOI 10.1137/1.9781611971484
[7]   A review of image denoising algorithms, with a new one [J].
Buades, A ;
Coll, B ;
Morel, JM .
MULTISCALE MODELING & SIMULATION, 2005, 4 (02) :490-530
[8]   New tight frames of curvelets and optimal representations of objects with piecewise C2 singularities [J].
Candès, EJ ;
Donoho, DL .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (02) :219-266
[9]  
Candès EJ, 2002, ANN STAT, V30, P784
[10]   Atomic decomposition by basis pursuit [J].
Chen, SSB ;
Donoho, DL ;
Saunders, MA .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 1998, 20 (01) :33-61