Learning nonlinear overcomplete representations for efficient coding
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Atomic Decomposition by Basis Pursuit
SIAM Review
Dictionary learning algorithms for sparse representation
Neural Computation
Learning Overcomplete Representations
Neural Computation
A simple test to check the optimality of a sparse signal approximation
Signal Processing - Sparse approximations in signal and image processing
Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
Method of optimal directions for frame design
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
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Neural Computation
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
Subset selection in noise based on diversity measure minimization
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Stable recovery of sparse overcomplete representations in the presence of noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
Adaptive wavelet thresholding for image denoising and compression
IEEE Transactions on Image Processing
Image coding using wavelet transform
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
`Neural-gas' network for vector quantization and its application to time-series prediction
IEEE Transactions on Neural Networks
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We propose a new algorithm for the design of overcomplete dictionaries for sparse coding, neural gas for dictionary learning (NGDL), which uses a set of solutions for the sparse coefficients in each update step of the dictionary. In order to obtain such a set of solutions, we additionally propose the bag of pursuits (BOP) method for sparse approximation. Using BOP in order to determine the coefficients of the dictionary, we show in an image encoding experiment that in case of limited training data and limited computation time the NGDL update of the dictionary performs better than the standard gradient approach that is used for instance in the Sparsenet algorithm, or other state-of-the-art methods for dictionary learning such as the method of optimal directions (MOD) or the widely used K-SVD algorithm. In an application to image reconstruction, dictionaries trained with this algorithm outperform not only overcomplete Haar-wavelets and overcomplete discrete cosine transformations, but also dictionaries obtained with widely used algorithms like K-SVD.