Practical Compact Deep Compressed Sensing

Recent years have witnessed the success of deep networks in compressed sensing (CS), which allows for a significant reduction in sampling cost and has gained growing attention since its inception. In this paper, we propose a new practical and compact network dubbed PCNet for general image CS. Specifically, in PCNet, a novel collaborative sampling operator is designed, which consists of a deep conditional filtering step and a dual-branch fast sampling step. The former learns an implicit representation of a linear transformation matrix into a few convolutions and first performs adaptive local filtering on the input image, while the latter then uses a discrete cosine transform and a scrambled block-diagonal Gaussian matrix to generate under-sampled measurements. Our PCNet is equipped with an enhanced proximal gradient descent algorithm-unrolled network for reconstruction. It offers flexibility, interpretability, and strong recovery performance for arbitrary sampling rates once trained. Additionally, we provide a deployment-oriented extraction scheme for single-pixel CS imaging systems, which allows for the convenient conversion of any linear sampling operator to its matrix form to be loaded onto hardware like digital micro-mirror devices. Extensive experiments on natural image CS, quantized CS, and self-supervised CS demonstrate the superior reconstruction accuracy and generalization ability of PCNet compared to existing state-of-the-art methods, particularly for high-resolution images.

I. Introduction

As a pioneering framework in signal processing, compressed sensing (CS) [1], [2] establishes a foundation to challenge the Nyquist-Shannon sampling theorem [3] and significantly reduce signal acquisition costs. It enables the accurate reconstruction of high-dimensional images from a small number of linear measurements and has led to a wide range of promising applications. These include single-pixel imaging [4], magnetic resonance imaging (MRI) [5], [6], computational tomography (CT) [7], and snapshot compressive imaging (SCI) [8], [9]. Additionally, CS has been applied to the source coding [10], [11] and encryption [12] of images and videos. In this work, we focus on general image CS problems, aiming to keep our contributions practical and extensible for the deployment of real-world CS systems.