On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems
Theoretical Computer Science
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Image Denoising Via Learned Dictionaries and Sparse representation
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inpainting and Zooming Using Sparse Representations
The Computer Journal
Robust-SL0 for stable sparse representation in noisy settings
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
A fast approach for overcomplete sparse decomposition based on smoothed l0 norm
IEEE Transactions on Signal Processing
Sparse approximation with adaptive dictionary for image prediction
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Sparse nonnegative matrix factorization with ℓ0-constraints
Neurocomputing
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Underdetermined blind source separation based on sparse representation
IEEE Transactions on Signal Processing
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On the Uniqueness of Nonnegative Sparse Solutions to Underdetermined Systems of Equations
IEEE Transactions on Information Theory
The In-Crowd Algorithm for Fast Basis Pursuit Denoising
IEEE Transactions on Signal Processing
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Sparse decomposition of a signal over an overcomplete dictionary has many applications including classification. One of the sparse solvers that has been proposed for finding the sparse solution of a spare decomposition problem (i.e., solving an underdetermined system of equations) is based on the Smoothed L0 norm (SL0). In some applications such as classification of visual data using sparse representation, the coefficients of the sparse solution should be in a specified range (e.g., non-negative solution). This paper presents a new approach based on the Constrained Smoothed L0 norm (CSL0) for solving sparse decomposition problems with non-negative constraint. The performance of the new sparse approach is evaluated on both simulated and real data. For the simulated data, the mean square error of the solution using the CSL0 is comparable to state-of-the-art sparse solvers. For real data, facial expression recognition via sparse representation is studied where the recognition rate using the CSL0 is better than other solver methods (in particular is about 4% better than the SL0).