Correction Algorithm of Sampling Effect and Its Application

TL;DR

This paper introduces a correction algorithm to mitigate sampling effects in imaging devices, significantly improving signal accuracy for both Gaussian and digitized images through high-precision correction techniques.

Contribution

It presents a novel correction algorithm that effectively reduces sampling-induced errors, enhancing image signal accuracy beyond traditional methods.

Findings

Accuracy increased by 10^6 for Gaussian images

Accuracy improved by 10^2 at 15x Shannon interpolation for digitized images

Accuracy reached 10^5 at 101x Shannon interpolation for digitized images

Abstract

The sampling effect of the imaging acquisition device is long considered to be a modulation process of the input signal, introducing additional error into the signal acquisition process. This paper proposes a correction algorithm for the modulation process that solves the sampling effect with high accuracy. We examine the algorithm with perfect continuous Gaussian images and selected digitized images, which indicate an accuracy increase of 106 for Gaussian images, 102 at 15 times of Shannon interpolation for digitized images, and 105 at 101 times of Shannon interpolation for digitized images. The accuracy limit of the Gaussian image comes from the truncation error, while the accuracy limit of the digitized images comes from their finite resolution, which can be improved by increasing the time of Shannon interpolation.