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Tác giả:

Ngôn ngữ: vie

Ký hiệu phân loại: 641.555 Timesaving cooking

Thông tin xuất bản: Vietnam Journal of Mathematics, 2014

Mô tả vật lý: 115-131

Bộ sưu tập: Metadata

ID: 495979

Much recent attention has been devoted to gradient descent algorithms where the steepest descent step size is replaced by a similar one from a previous iteration or gets updated only once every second step, thus forming a faster gradient descent method. For unconstrained convex quadratic optimization these methods can converge much faster than steepest descent. But the context of interest here is application to certain ill-posed inverse problems, where the steepest descent method is known to have a smoothing, regularizing effect, and where a strict optimization solution is not necessary. Specifically, in this paper the authors examine the effect of replacing steepest descent by a faster gradient descent algorithm in the practical context of image deblurring and denoising tasks. The authors also propose several highly efficient schemes for carrying out these tasks independently of the step size selection, as well as a scheme for the case where both blur and significant noise are present. In the above context there are situations where many steepest descent steps are required, thus building slowness into the solution procedure. The general conclusion regarding gradient descent methods is that in such cases the faster gradient descent methods offer substantial advantages. In other situations where no such slowness buildup arisd the steepest descent method can still be very effective.
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