Analysis Based Blind Compressive Sensing

TL;DR

This paper introduces a novel blind compressive sensing method that adaptively learns an analysis operator during signal reconstruction, effectively handling various noise types through a geometric conjugate gradient optimization.

Contribution

It presents an adaptive algorithm for blind compressive sensing based on the co-sparse analysis model, improving reconstruction under different noise conditions.

Findings

Effective reconstruction with Gaussian noise

Robust to impulsive noise

Adaptive operator learning enhances performance

Abstract

In this work we address the problem of blindly reconstructing compressively sensed signals by exploiting the co-sparse analysis model. In the analysis model it is assumed that a signal multiplied by an analysis operator results in a sparse vector. We propose an algorithm that learns the operator adaptively during the reconstruction process. The arising optimization problem is tackled via a geometric conjugate gradient approach. Different types of sampling noise are handled by simply exchanging the data fidelity term. Numerical experiments are performed for measurements corrupted with Gaussian as well as impulsive noise to show the effectiveness of our method.