Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Image Representation Using 2D Gabor Wavelets
IEEE Transactions on Pattern Analysis and Machine Intelligence
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics
Dictionary learning algorithms for sparse representation
Neural Computation
Convex Optimization
Efficient Coding of Time-Relative Structure Using Spikes
Neural Computation
Learning Overcomplete Representations
Neural Computation
Sparse audio representations using the MCLT
Signal Processing - Sparse approximations in signal and image processing
Convergence Theorems for Generalized Alternating Minimization Procedures
The Journal of Machine Learning Research
Practical gammatone-like filters for auditory processing
EURASIP Journal on Audio, Speech, and Music Processing
Dictionary learning for sparse approximations with the majorization method
IEEE Transactions on Signal Processing
-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
IEEE Transactions on Signal Processing
An affine scaling methodology for best basis selection
IEEE Transactions on Signal Processing
Sparse signal reconstruction from limited data using FOCUSS: are-weighted minimum norm algorithm
IEEE Transactions on Signal Processing
A Geometrical Study of Matching Pursuit Parametrization
IEEE Transactions on Signal Processing - Part I
Fast matching pursuit with a multiscale dictionary of Gaussianchirps
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Union of MDCT Bases for Audio Coding
IEEE Transactions on Audio, Speech, and Language Processing
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
Designing structured tight frames via an alternating projection method
IEEE Transactions on Information Theory
On the exponential convergence of matching pursuits in quasi-incoherent dictionaries
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
Adaptive compressed sensing of speech signal based on data-driven dictionary
APCC'09 Proceedings of the 15th Asia-Pacific conference on Communications
Dictionary learning for sparse representations: a Pareto curve root finding approach
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
| Hi-index | 35.68 |
This paper introduces a new dictionary design method for sparse coding of a class of signals. It has been shown that one can sparsely approximate some natural signals using an overcomplete set of parametric functions. A problem in using these parametric dictionaries is how to choose the parameters. In practice, these parameters have been chosen by an expert or through a set of experiments. In the sparse approximation context, it has been shown that an incoherent dictionary is appropriate for the sparse approximation methods. In this paper, we first characterize the dictionary design problem, subject to a constraint on the dictionary. Then we briefly explain that equiangular tight frames have minimum coherence. The complexity of the problem does not allow it to be solved exactly. We introduce a practical method to approximately solve it. Some experiments show the advantages one gets by using these dictionaries.