Separable Cosparse Analysis Operator Learning

TL;DR

This paper introduces a novel algorithm for learning separable cosparse analysis operators that efficiently handle multidimensional data, such as 3D MRI scans, by exploiting inherent data structure to reduce computational costs.

Contribution

The paper proposes a new method for learning structured cosparse analysis operators that respect data multidimensionality, improving efficiency over traditional vectorized approaches.

Findings

Effective on volumetric data like 3D MRI scans

Reduces computational cost by exploiting data structure

Demonstrates promising results in multidimensional data analysis

Abstract

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose an algorithm for learning a cosparse Analysis Operator that adheres to the preexisting structure of the data, and thus allows for a very efficient implementation. This is achieved by enforcing a separable structure on the learned operator. Our learning algorithm is able to deal with multidimensional data of arbitrary order. We evaluate our method on volumetric data at the example of three-dimensional MRI scans.