Practical configurations to recover the regularized least-squares solution

Ramakrishnan Sundaram

doi:10.1117/12.365855

18 October 1999 Practical configurations to recover the regularized least-squares solution

Ramakrishnan Sundaram

Proceedings Volume 3808, Applications of Digital Image Processing XXII; (1999) https://doi.org/10.1117/12.365855
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Several engineering applications are concerned with the accurate and efficient identification of the least-squares (LS) solution. The computational and storage requirements to determine the LS solution become prohibitively large as the dimensions of the problem grow. This paper develops an algorithm which receives the least squares solution based on a steepest descent formulation. Among the advantages of this approach are improvements in computational and resource management, and ease of hardware implementation. The gradient matrix is evaluated using 2-D linear convolutions and an in- place update strategy. An iterative procedure is outlined and the regularized and unregularized LS solutions can be recovered. The extent of regularization is suitably controlled and imposes some constraints on the step size for steepest descent. The proposed approach is examined in the context of digital image restoration from spatially invariant linear blur degradation and compared with alternate strategies performing LS recovery.

Citation Download Citation

Ramakrishnan Sundaram "Practical configurations to recover the regularized least-squares solution", Proc. SPIE 3808, Applications of Digital Image Processing XXII, (18 October 1999); https://doi.org/10.1117/12.365855

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KEYWORDS

Convolution

Image restoration

Algorithm development

Error analysis

Matrices

Chemical elements

Data processing

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