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K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation
In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described byExpand
$rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, the K-SVD algorithm, an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. Expand
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
This work addresses the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image, and uses the K-SVD algorithm to obtain a dictionary that describes the image content effectively. Expand
On Single Image Scale-Up Using Sparse-Representations
This paper deals with the single image scale-up problem using sparse-representation modeling, and assumes a local Sparse-Land model on image patches, serving as regularization, to recover an original image from its blurred and down-scaled noisy version. Expand
Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing
This textbook introduces sparse and redundant representations with a focus on applications in signal and image processing and how to use the proper model for tasks such as denoising, restoration, separation, interpolation and extrapolation, compression, sampling, analysis and synthesis, detection, recognition, and more. Expand
Fast and robust multiframe super resolution
This paper proposes an alternate approach using L/sub 1/ norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models and demonstrates its superiority to other super-resolution methods. Expand
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ1 minimization
  • D. Donoho, Michael Elad
  • Computer Science, Medicine
  • Proceedings of the National Academy of Sciences…
  • 21 February 2003
This article obtains parallel results in a more general setting, where the dictionary D can arise from two or several bases, frames, or even less structured systems, and sketches three applications: separating linear features from planar ones in 3D data, noncooperative multiuser encoding, and identification of over-complete independent component models. Expand
Stable recovery of sparse overcomplete representations in the presence of noise
This paper establishes the possibility of stable recovery under a combination of sufficient sparsity and favorable structure of the overcomplete system and shows that similar stability is also available using the basis and the matching pursuit algorithms. Expand
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
The aim of this paper is to introduce a few key notions and applications connected to sparsity, targeting newcomers interested in either the mathematical aspects of this area or its applications. Expand
Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit
An e‐cient implementation of the K-SVD algorithm is discussed, which both accelerates it and reduces its memory consumption and the Batch-OMP implementation, which is useful for a variety of sparsity-based techniques which involve coding large numbers of signals. Expand