OPED reconstruction algorithm for limited angle problem

TL;DR

The paper introduces an OPED-based reconstruction algorithm that effectively handles limited angle problems by completing the sine transform data through solving positive definite linear systems, demonstrated with numerical examples.

Contribution

It presents a novel method for limited angle image reconstruction by completing sine transform data, enhancing the OPED algorithm's capabilities.

Findings

Successful reconstruction in limited angle scenarios

Use of positive definite systems for data completion

Numerical examples validate the approach

Abstract

The structure of the reconstruction algorithm OPED permits a natural way to generate additional data, while still preserving the essential feature of the algorithm. This provides a method for image reconstruction for limited angel problems. In stead of completing the set of data, the set of discrete sine transforms of the data is completed. This is achieved by solving systems of linear equations that have, upon choosing appropriate parameters, positive definite coefficient matrices. Numerical examples are presented.