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Blockwise conjugate gradient methods for image reconstruction in volumetric CT.

W Qiu¹, D Titley-Peloquin, M Soleimani

¹Department of Electronic and Electrical Engineering, University of Bath, Bath BA2 7AY, UK.

Computer Methods and Programs in Biomedicine

|February 14, 2012

Summary

Cone beam computed tomography (CBCT) image reconstruction can be improved using the LSQR algorithm. This method efficiently handles large matrices, overcoming memory limitations for better image quality in image guided radiation therapy.

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Area of Science:

Medical Imaging
Computational Imaging
Radiation Oncology

Background:

Cone beam computed tomography (CBCT) is crucial for image guided radiation therapy (IGRT).
Filtered back projection is the standard reconstruction algorithm, but has limitations.
Conjugate gradients (CG) algorithms are effective for large, sparse linear systems but underutilized in CBCT.

Purpose of the Study:

To implement and evaluate the CG-type algorithm LSQR for CBCT reconstruction.
To address the computational challenge of large matrices in CBCT reconstruction.
To improve CBCT image quality without requiring advanced hardware.

Main Methods:

Implemented the LSQR algorithm for CBCT reconstruction.
Developed a blockwise storage and matrix-vector multiplication strategy for the large weighting matrix A.
Incorporated Tikhonov regularization within the blockwise LSQR framework.

Main Results:

The blockwise LSQR implementation successfully utilized the full weighting matrix A, overcoming memory constraints.
This approach enabled high-quality CBCT reconstruction on standard computers.
Tikhonov regularization further enhanced the reconstructed image quality.

Conclusions:

The LSQR algorithm, with blockwise matrix handling, is a viable and effective method for CBCT reconstruction.
This technique overcomes significant computational challenges, improving image quality for IGRT.
Blockwise implementation allows for the use of regularization methods like Tikhonov for superior results.