# Multichannel reconstruction from nonuniform samples with application to image recovery

## TL;DR

This paper develops a theory for multichannel interpolation from nonuniform samples, enabling improved image recovery and interpolation accuracy, especially in highly corrupted images, by leveraging multiple sampling models and derivatives.

## Contribution

It introduces a novel multichannel interpolation framework for nonuniform samples, extending previous uniform sampling methods and applying it to enhance image reconstruction quality.

## Key findings

- Effective interpolation from nonuniform samples demonstrated
- Superior image recovery compared to median filter methods
- Lower errors in highly corrupted image reconstruction

## Abstract

The multichannel trigonometric reconstruction from uniform samples was proposed recently. It not only makes use of multichannel information about the signal but is also capable to generate various kinds of interpolation formulas according to the types and amounts of the collected samples. The paper presents the theory of multichannel interpolation from nonuniform samples. Two distinct models of nonuniform sampling patterns are considered, namely recurrent and generic nonuniform sampling. Each model involves two types of samples: nonuniform samples of the observed signal and its derivatives. Numerical examples and quantitative error analysis are provided to demonstrate the effectiveness of the proposed algorithms. Additionally, the proposed algorithm for recovering highly corrupted images is also investigated. In comparison with the median filter and correction operation treatment, our approach produces superior results with lower errors.