题 目： Proximal iterative hard thresholding for sparse optimization
摘 要：The iterative thresholding algorithms, both soft and hard thresholding, are widely adopted for sparsity promoting in imaging and data science. The analysis of iterative soft thresholding algorithms has been well studied under the framework of convexity and operator splitting methods and inspired many algorithms for related minimization problems. However, iterative hard thresholding methods are less understood due to its non-convexity and discontinuity, although there are some studies related to sparse signal recovery and image restorations. We considered the minimization of the sum of L0-norm and a smooth function arising from image restoration and sparse learning. We first proposed an extrapolated proximal iterative hard thresholding (EPIHT) algorithm and its variant with line-search. Under the theoretical framework of Kurdyka-Lojasiewicz (KL) property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems demonstrate the improvement of L0-norm based regularization models over some prevailing ones. We further considered the minimization of the sum of L0-norm and a convex smooth function under box constraint and designed an accelerated extrapolated proximal algorithm. The global convergence to a local minimizer of this algorithm is also established based on the convexity of the first function and the property of L0 function, while without using the tool of KL property. Numerical experiments on compressive sensing and sparse logistic regression showed the effectiveness of the latter one compared to other multi-steps algorithms for L0 minimization.
时 间：2018年12月13日 上午1:50