Welcome to Dictionary Learning Toolbox’s documentation!

This toolbox solves several Dictionary Learning problems, the basic one being

\begin{split}\begin{align} \min _{D, \mathbf{X}} & \|\mathbf{Y}-\mathbf{D} \mathbf{X}\|_{F}^{2} \\ \text { s.t. } & \left\|\mathbf{x}_{\ell}\right\|_{0} \leq s, \ell=1: N \\ & \left\|\mathbf{d}_{j}\right\|=1, j=1: n \label{eq-dl} \end{align}\end{split}

where $$\mathbf{Y} \in \mathbb{R}^{m \times N}$$ is a given set of $$N$$ signals, each of size $$m$$, $$\mathbf{D} \in \mathbb{R}^{m \times n}$$ is the trained dictionary, $$\mathbf{X} \in \mathbb{R}^{n \times N}$$ is the sparse representation matrix (or sparse codes) and $$s$$ represents the sparsity level.