# Block Compressive Sensing of Image and Video with Nonlocal Lagrangian Multiplier and Patch-based Sparse Representation

## TL;DR

This paper introduces a novel block compressive sensing recovery method for images and videos that enhances quality by using multi-block gradients, denoised Lagrangian multipliers, and patch-based sparsity, effectively reducing artifacts and preserving details.

## Contribution

It proposes a new recovery technique combining multi-block gradient processing, a denoised Lagrangian multiplier, and patch-based sparse representation for improved image and video reconstruction.

## Key findings

- Enhanced image and video quality in terms of objective metrics.
- Effective reduction of artifacts and preservation of details.
- Exploitation of spatial and temporal similarities in videos.

## Abstract

Although block compressive sensing (BCS) makes it tractable to sense large-sized images and video, its recovery performance has yet to be significantly improved because its recovered images or video usually suffer from blurred edges, loss of details, and high-frequency oscillatory artifacts, especially at a low subrate. This paper addresses these problems by designing a modified total variation technique that employs multi-block gradient processing, a denoised Lagrangian multiplier, and patch-based sparse representation. In the case of video, the proposed recovery method is able to exploit both spatial and temporal similarities. Simulation results confirm the improved performance of the proposed method for compressive sensing of images and video in terms of both objective and subjective qualities.