Learning Sparse Overcomplete Codes for Images
Journal of VLSI Signal Processing Systems
Nonlinear underdetermined blind signal separation using Bayesian neural network approach
Digital Signal Processing
Learning Sparse Overcomplete Codes for Images
Journal of VLSI Signal Processing Systems
Sparse coding via thresholding and local competition in neural circuits
Neural Computation
Review of user parameter-free robust adaptive beamforming algorithms
Digital Signal Processing
IEEE Transactions on Signal Processing
Sparse image reconstruction for molecular imaging
IEEE Transactions on Image Processing
Stagewise weak gradient pursuits
IEEE Transactions on Signal Processing
An iterative Bayesian algorithm for sparse component analysis in presence of noise
IEEE Transactions on Signal Processing
Variance-component based sparse signal reconstruction and model selection
IEEE Transactions on Signal Processing
Bayesian compressive sensing using Laplace priors
IEEE Transactions on Image Processing
Computationally efficient sparse Bayesian learning via belief propagation
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Modified-CS: modifying compressive sensing for problems with partially known support
IEEE Transactions on Signal Processing
Computationally efficient sparse Bayesian learning via belief propagation
IEEE Transactions on Signal Processing
Range-doppler imaging via forward-backward sparse bayesian learning
IEEE Transactions on Signal Processing
Sparse Bayesian learning for the Laplace transform inversion in dynamic light scattering
Journal of Computational and Applied Mathematics
Efficient Sensing Topology Management for Spatial Monitoring with Sensor Networks
Journal of Signal Processing Systems
Compression and denoising using l0-norm
Computational Optimization and Applications
Optimization with Sparsity-Inducing Penalties
Foundations and Trends® in Machine Learning
Trench-Zohar inversion for SAR sensor network 3-D imaging based on compressive sensing
International Journal of Sensor Networks
Detection of sparse targets with structurally perturbed echo dictionaries
Digital Signal Processing
Gaussian Kullback-Leibler approximate inference
The Journal of Machine Learning Research
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Sparse Bayesian learning (SBL) and specifically relevance vector machines have received much attention in the machine learning literature as a means of achieving parsimonious representations in the context of regression and classification. The methodology relies on a parameterized prior that encourages models with few nonzero weights. In this paper, we adapt SBL to the signal processing problem of basis selection from overcomplete dictionaries, proving several results about the SBL cost function that elucidate its general behavior and provide solid theoretical justification for this application. Specifically, we have shown that SBL retains a desirable property of the ℓ0-norm diversity measure (i.e., the global minimum is achieved at the maximally sparse solution) while often possessing a more limited constellation of local minima. We have also demonstrated that the local minima that do exist are achieved at sparse solutions. Later, we provide a novel interpretation of SBL that gives us valuable insight into why it is successful in producing sparse representations. Finally, we include simulation studies comparing sparse Bayesian learning with basis pursuit and the more recent FOCal Underdetermined System Solver (FOCUSS) class of basis selection algorithms. These results indicate that our theoretical insights translate directly into improved performance.