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Sparse Coding via Thresholding and Local Competition in Neural Circuits
TLDR
A locally competitive algorithm (LCA) is described that solves a collection of sparse coding principles minimizing a weighted combination of mean-squared error and a coefficient cost function to produce coefficients with sparsity levels comparable to the most popular centralized sparse coding algorithms while being readily suited for neural implementation.
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Learning Sparse Codes for Hyperspectral Imagery
TLDR
This work modified an existing unsupervised learning approach and applied it to HSI data to learn an optimal sparse coding dictionary, which improves the performance of a supervised classification algorithm, both in terms of the classifier complexity and generalization from very small training sets.
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The Restricted Isometry Property for Random Block Diagonal Matrices
View PDF on arXiv
All-optical nanoscale pH meter.
We show that an Au nanoshell with a pH-sensitive molecular adsorbate functions as a standalone, all-optical nanoscale pH meter that monitors its local environment through the pH-dependent…
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Convergence and Rate Analysis of Neural Networks for Sparse Approximation
TLDR
An analysis of the Locally Competitive Algorithm (LCA), which is a Hopfield-style neural network that efficiently solves sparse approximation problems, shows that the LCA has desirable convergence properties, such as stability and global convergence to the optimum of the objective function when it is unique.
View on IEEE
Locally Competitive Algorithms for Sparse Approximation
TLDR
This work presents a class of locally competitive algorithms (LCAs) that correspond to a collection of sparse approximation principles minimizing a weighted combination of reconstruction MSE and a coefficient cost function that can produce coefficients for video sequences that are more regular than the coefficients produced by greedy algorithms.
View on IEEE
Visual Nonclassical Receptive Field Effects Emerge from Sparse Coding in a Dynamical System
TLDR
The results show that the sparse coding hypothesis, when coupled with a biophysically plausible implementation, can provide a unified high-level functional interpretation to many response properties that have generally been viewed through distinct mechanistic or phenomenological models.
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Sparsity penalties in dynamical system estimation
TLDR
An overview of different methods for incorporating sparsity into the dynamic model, a presentation of algorithms that unify the support and coefficient estimation, and a demonstration that these suboptimal schemes can actually show some performance improvements over standard optimal methods that use an impoverished model.
View on IEEE
Concentration of Measure for Block Diagonal Matrices With Applications to Compressive Signal Processing
TLDR
It is shown that for the best case signals, both types of block diagonal matrices can offer concentration performance on par with their unstructured, i.i.d. counterparts, and applications in ensuring stable embeddings for various signal families and in establishing performance guarantees for solving various signal processing tasks directly in the compressed domain are discussed.
View on IEEE
Optimal Sparse Approximation with Integrate and Fire Neurons
TLDR
It is shown that the firing rate of the Spiking LCA converges on the same solution as the analog LCA, with an error inversely proportional to the sampling time, and that when using more biophysically realistic parameters in the neurons, the gain function encourages additional ℓ(0)-norm sparsity in the encoding, relative both to ideal neurons and digital solvers.
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