# An efficient algorithm for compression-based compressed sensing

## TL;DR

This paper introduces a new low-complexity iterative algorithm called C-GD that leverages generic compression codes for efficient compressed sensing recovery, bridging the gap between simple structures and advanced compression-based signals.

## Contribution

The paper proposes the C-GD algorithm, enabling the use of complex compression codes in compressed sensing recovery with theoretical guarantees and robustness to noise.

## Key findings

- C-GD achieves state-of-the-art imaging performance with JPEG2000.
- Theoretical analysis shows convergence and measurement bounds based on rate-distortion.
- C-GD is robust to additive white Gaussian noise.

## Abstract

Modern image and video compression codes employ elaborate structures existing in such signals to encode them into few number of bits. Compressed sensing recovery algorithms on the other hand use such signals' structures to recover them from few linear observations. Despite the steady progress in the field of compressed sensing, structures that are often used for signal recovery are still much simpler than those employed by state-of-the-art compression codes. The main goal of this paper is to bridge this gap through answering the following question: Can one employ a given compression code to build an efficient (polynomial time) compressed sensing recovery algorithm? In response to this question, the compression-based gradient descent (C-GD) algorithm is proposed. C-GD, which is a low-complexity iterative algorithm, is able to employ a generic compression code for compressed sensing and therefore elevates the scope of structures used in compressed sensing to those used by compression codes. The convergence performance of C-GD and its required number of measurements in terms of the rate-distortion performance of the compression code are theoretically analyzed. It is also shown that C-GD is robust to additive white Gaussian noise. Finally, the presented simulation results show that combining C-GD with commercial image compression codes such as JPEG2000 yields state-of-the-art performance in imaging applications.