# Dictionary Learning, Blind Deconvolution, Deep Learning

Learning dictionaries/atomic sets that induce structured representation on data. Applications are still explosively emerging, especially of deep learning, where one allows multi-level nonlinear cascading of representation. Hence formulations to the problems are fairly diverse. We will roughly organize the references according to the problem they try to solve, concentrated on recent literature of theoretical nature. (Update: May 19 2017)

[S] indicates my contribution.

## Theory

### $\mathbf{Y} = \mathbf{A} \mathbf{X}$, $\mathbf{A}$ Square, Invertible, Global Recovery

This problem can be reduced to a sequence of problems, each taking the form of finding sparsest vector in a linear subspace. See also Structured Element Pursuit.

### $\mathbf{Y} = \mathbf{A} \mathbf{X}$ Local Correctness

1. On the Local Correctness of $\ell^1$ Minimization for Dictionary Learning (2011, $\mathbf{A}$ general)
2. Dictionary Identification - Sparse Matrix-Factorisation via $\ell^1$-Minimisation (2009, $\mathbf{A}$ square)

## Algorithms and Applications

### Dictionary Learning

1. To get a taste of the applications of dictionary learning in signal and image processing (compression in these areas demands good bases/dictionaries), see the book by Michael Elad: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing

### Deep Learning

1. Scattering Page maintained by Stephane Mallat’s group

Disclaimer - This page is meant to serve a hub for references on this problem, and does not represent in any way personal endorsement of papers listed here. So I do not hold any responsibility for quality and technical correctness of each paper listed here. The reader is advised to use this resource with discretion.

If you’d like your paper to be listed here - Just drop me a few lines via email (which can be found on “Welcome” page). If you don’t bother to spend a word, just deposit your paper on arXiv. I get email alert about new animals there every morning,  and will be happy to hunt one for this zoo if it seems fit.