Dictionary construction in sparse methods for image restoration

Journal Article · Fri Jan 01 04:00:00 EST 2010

OSTI ID:983230

Wohlberg, Brendt ^[1]

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1. Los Alamos National Laboratory

Sparsity-based methods have achieved very good performance in a wide variety of image restoration problems, including denoising, inpainting, super-resolution, and source separation. These methods are based on the assumption that the image to be reconstructed may be represented as a superposition of a few known components, and the appropriate linear combination of components is estimated by solving an optimization such as Basis Pursuit De-Noising (BPDN). Considering that the K-SVD constructs a dictionary which has been optimised for mean performance over a training set, it is not too surprising that better performance can be achieved by selecting a custom dictionary for each individual block to be reconstructed. The nearest neighbor dictionary construction can be understood geometrically as a method for estimating the local projection into the manifold of image blocks, whereas the K-SVD dictionary makes more sense within a source-coding framework (it is presented as a generalization of the k-means algorithm for constructing a VQ codebook), is therefore, it could be argued, less appropriate in principle, for reconstruction problems. One can, of course, motivate the use of the K-SVD in reconstruction application on practical grounds, avoiding the computational expense of constructing a different dictionary for each block to be denoised. Since the performance of the nearest neighbor dictionary decreases when the dictionary becomes sufficiently large, this method is also superior to the approach of utilizing the entire training set as a dictionary (and this can also be understood within the image block manifold model). In practical terms, the tradeoff is between the computational cost of a nearest neighbor search (which can be achieved very efficiently), or of increased cost at the sparse optimization.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 983230
• Report Number(s): LA-UR-10-00042; LA-UR-10-42
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
CONSTRUCTION
OPTIMIZATION
PERFORMANCE
TRAINING