Newton-step-based Hard Thresholding Algorithms

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• Nan Meng (University of Birmingham)
• Wednesday 04 December 2019, 12:00-13:00
• Strathcona, SR5.

If you have a question about this talk, please contact Sergey Sergeev.

Compressive sensing (CS) has been applied in the field of image processing, pattern recognition and medical applications. A class of algorithms, known as hard thresholding algorithms and first proposed by Blumensath and Davies, have been investigated heavily in CS. The existing hard thresholding algorithms, such as the iterative hard thresholding (IHT) and hard thresholding pursuit (HTP), utilize the gradient steepest descent direction. In solving nonlinear optimization problems, Newton’s method is also great of importance. We would consider to apply Newton’s method to solve the k-sparse problem. We apply it by modifying the Hessian with a parameter since the original Hessian is non-invertible. In this case, we establish sufficient conditions for the convergence of the NSIHT algorithm and NSHTP algorithm. Afterwards, we investigate the numerical performance of the class of Newton-step-based hard thresholding algorithms.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

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• Optimisation and Numerical Analysis Seminars
• School of Mathematics events
• Strathcona, SR5

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