
Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices
Data encoded as symmetric positive definite (SPD) matrices frequently ar...
read it

Robust Compressed Sensing and Sparse Coding with the Difference Map
In compressed sensing, we wish to reconstruct a sparse signal x from obs...
read it

DeeplySparse Signal rePresentations (DS^2P)
The solution to the regularized leastsquares problem min_x∈R^p+1/2yAx_...
read it

Globally VarianceConstrained Sparse Representation for Image Set Compression
Sparse representation presents an efficient approach to approximately re...
read it

Convolutional Dictionary Learning
Convolutional sparse representations are a form of sparse representation...
read it

Interactive Character Posing by Sparse Coding
Character posing is of interest in computer animation. It is difficult d...
read it

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements
This paper addresses the problem of distributed coding of images whose c...
read it
Dense and Sparse Coding: Theory and Architectures
The sparse representation model has been successfully utilized in a number of signal and image processing tasks; however, recent research has highlighted its limitations in certain deeplearning architectures. This paper proposes a novel dense and sparse coding model that considers the problem of recovering a dense vector 𝐱 and a sparse vector 𝐮 given linear measurements of the form 𝐲 = 𝐀𝐱+𝐁𝐮. Our first theoretical result proposes a new natural geometric condition based on the minimal angle between subspaces corresponding to the measurement matrices 𝐀 and 𝐁 to establish the uniqueness of solutions to the linear system. The second analysis shows that, under mild assumptions and sufficient linear measurements, a convex program recovers the dense and sparse components with high probability. The standard RIPless analysis cannot be directly applied to this setup. Our proof is a nontrivial adaptation of techniques from anisotropic compressive sensing theory and is based on an analysis of a matrix derived from the measurement matrices 𝐀 and 𝐁. We begin by demonstrating the effectiveness of the proposed model on simulated data. Then, to address its use in a dictionary learning setting, we propose a dense and sparse autoencoder (DenSaE) that is tailored to it. We demonstrate that a) DenSaE denoises natural images better than architectures derived from the sparse coding model (𝐁𝐮), b) training the biases in the latter amounts to implicitly learning the 𝐀𝐱 + 𝐁𝐮 model, and c) 𝐀 and 𝐁 capture low and highfrequency contents, respectively.
READ FULL TEXT
Comments
There are no comments yet.