Dictionary Learning

Dictionary learning is a key problem in computational neuroscience, machine learning, computer vision, and image processing. Its core objective is to find an appropriate basis from the given data. Specifically, in the dictionary learning problem, we obtain samples of the form \( y = Ax \), where \( y \in \mathbb{R}^n \) is a random vector, \( A \) is an unknown dictionary matrix, and \( x \) is sampled from an unknown distribution of sparse vectors. The goal of the task is to approximately recover this dictionary matrix \( A \) so as to effectively represent and analyze the data.