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

Area of Science:

• Medical Imaging
• Computational Imaging
• Tomographic Reconstruction

Background:

• Addresses the computational challenges of incomplete view tomography (sparse and limited-angle).
• Highlights limitations of traditional Landweber-type methods requiring extensive matrix-vector multiplications.

Purpose of the Study:

• Develops an efficient discretization approach for Landweber-type methods.
• Aims to minimize storage and computational demands by leveraging the Radon transform structure.

Main Methods:

• Proves the normal operator of the incomplete view Radon transform is a compact convolution operator.
• Derives the convolution kernel and applies pixel basis discretization.
• Introduces a fast, accurate, low-storage discretized convolution operation.

Main Results:

• Achieves 1-5dB PSNR improvement and reduces computation time by two-thirds for limited-angle data.
• Generates high-quality reconstructed images for sparse view data.
• Demonstrates significant efficiency gains over traditional methods.

Conclusions:

• Landweber-type methods with the proposed discretization are effective for incomplete view tomography.
• The novel approach enhances reconstruction accuracy and efficiency.
• Offers a practical solution for sparse and limited-angle tomographic reconstruction.