# Convolutional Sparse Representations with Gradient Penalties

## TL;DR

This paper investigates convolutional sparse representations for image denoising, showing that gradient penalties on coefficient maps significantly improve their performance over traditional block-based methods.

## Contribution

It introduces gradient penalties into convolutional sparse coding, enhancing noise removal capabilities beyond existing block-based approaches.

## Key findings

- Gradient penalties improve convolutional sparse coding performance.
- Convolutional representations with penalties outperform block-based methods in noise removal.
- Gradient-penalized models achieve superior image reconstruction quality.

## Abstract

While convolutional sparse representations enjoy a number of useful properties, they have received limited attention for image reconstruction problems. The present paper compares the performance of block-based and convolutional sparse representations in the removal of Gaussian white noise. While the usual formulation of the convolutional sparse coding problem is slightly inferior to the block-based representations in this problem, the performance of the convolutional form can be boosted beyond that of the block-based form by the inclusion of suitable penalties on the gradients of the coefficient maps.