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Abstract

Background

We study the reconstruction problem for incomplete view tomography, including sparse view tomography and limited angle tomography, by the Landweber iteration and its accelerated version. Traditional implementations of these Landweber-type iterative methods necessitate multiple large-scale matrix-vector multiplications, which in turn require substantial time and storage resources.

Objective

This paper aims to develop and test a novel and efficient discretization approach for a class of Landweber-type methods that minimizes storage requirements by incorporating the specific structure of the incomplete view Radon transform.

Methods

We prove that the normal operator of incomplete view Radon transform in these methods is a compact convolution operator, and derive the explicit representation of its convolution kernel. Discretized by the pixel basis, these Landweber-type iterative methods can be implemented quickly and accurately by introducing a discretized convolution operation between two small-scale matrices with minimal storage requirements.

Results

For the simulated complete and limited angle data, the reconstruction results using various Landweber-type methods with our proposed discretization scheme achieve a 1-5dB improvement in PSNR and require one-third of computation time compared to the traditional approach. For the simulated sparse view data, our discretization scheme yields a valid image with the highest PSNR.

Conclusions

The Landweber-type iterative methods, when combined with our proposed discretization approach based on the Radon transform, are effective for addressing the incomplete view tomography problem.

Keywords

incomplete view tomography Radon transform Landweber-type iteration convolution representation discretization

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A class of Landweber-type iterative methods based on the Radon transform for incomplete view tomography

Abstract

Background

Objective

Methods

Results

Conclusions

Keywords

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References