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Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.

T Nikazad¹, R Davidi, G T Herman

¹Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran.

Inverse Problems

|February 27, 2013

Summary

This study introduces accelerated block-iterative projection methods that efficiently solve linear equations, even with perturbations. These methods offer significant speed-ups for image reconstruction and medical imaging tasks.

Keywords:

block-iterative algorithms image reconstruction from projections perturbation resilience superiorization total variation

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Area of Science:

Numerical analysis
Applied mathematics
Computational imaging

Background:

Block-iterative projection methods are used for solving linear systems.
Perturbations can affect the convergence and accuracy of iterative methods.
Image reconstruction and medical imaging often involve solving large linear systems.

Purpose of the Study:

To analyze the convergence properties of accelerated perturbation-resilient block-iterative projection methods.
To demonstrate the efficiency and applicability of these methods in image reconstruction and medical diagnosis.
To establish the superiority of accelerated methods over unaccelerated versions.

Main Methods:

Development and theoretical analysis of accelerated perturbation-resilient block-iterative projection methods.
Mathematical proofs of convergence to a fixed point under summable perturbations.
Application and empirical validation on image reconstruction and X-ray CT data.

Main Results:

Convergence is proven to a fixed point of an operator, even with summable perturbations.
For consistent systems, the limit point is a solution; for inconsistent systems, it's a weighted least squares solution.
An order of magnitude speed-up was achieved in image reconstruction; improved tumor detection accuracy in CT data.

Conclusions:

The proposed methods offer robust and efficient solutions for linear systems with perturbations.
Accelerated algorithms provide significant performance gains in computational imaging and medical applications.
These methods represent a substantial advancement for solving inverse problems in science and engineering.