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.
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