Properties on n-dimensional convolution for image deconvolution

TL;DR

This paper explores properties of N-dimensional convolution and introduces a new image deconvolution method leveraging these properties, which is efficient and suitable for GPU implementation, showing comparable results to existing techniques.

Contribution

The paper presents novel properties of N-dimensional convolution and a new deconvolution method based on these properties, enhancing efficiency and GPU compatibility.

Findings

Method achieves similar deconvolution quality to state-of-the-art techniques.

Core calculation is simple convolution, enabling GPU acceleration.

Applicable to large-scale image processing tasks.

Abstract

Convolution system is linear and time invariant, and can describe the optical imaging process. Based on convolution system, many deconvolution techniques have been developed for optical image analysis, such as boosting the space resolution of optical images, image denoising, image enhancement and so on. Here, we gave properties on N-dimensional convolution. By using these properties, we proposed image deconvolution method. This method uses a series of convolution operations to deconvolute image. We demonstrated that the method has the similar deconvolution results to the state-of-art method. The core calculation of the proposed method is image convolution, and thus our method can easily be integrated into GPU mode for large-scale image deconvolution.