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題目：The springback penalty for robust signal recovery

報告人：安聰沛 西南財經(jīng)大學(xué) 副教授

時間:  9月26日（周二）下午16: 20-17: 10

地點：30456

摘要：We propose a new penalty, the springback penalty, for constructing models to recover an unknown signal from incomplete and inaccurate measurements.  Mathematically, the springback penalty is a weakly convex function. It bears various theoretical and computational advantages of both the benchmark convex 1 penalty  and many of its non-convex surrogates that have been well studied in the literature. We establish the exact and stable recovery theory for the recovery model using the springback penalty for both sparse and nearly sparse signals, respectively, and derive an easily implementable di?erence-of-convex algorithm. In particular, we show its theoretical superiority to some existing models with a sharper recovery bound for some scenarios where the level of measurement noise is large or the amount of measurements is limited. We also demonstrate its numerical robustness regardless of the varying coherence of the sensing matrix. The springback penalty is particularly favorable for the scenario where the incomplete and inaccurate measurements are collected by coherence-hidden or -static sensing hardware due to its theoretical guarantee of recovery with severe measurements, computational tractability, and numerical robustness for ill-conditioned sensing matrices.

個人簡介：安聰沛, 本科、碩士畢業(yè)于中南大學(xué)，博士畢業(yè)于香港理工大學(xué)，現(xiàn)為西南財經(jīng)大學(xué)kaiyun開云官方網(wǎng)站副教授、博導(dǎo)。入選四川省"天府峨眉計劃",美國《數(shù)學(xué)評論》評論員，主持過三項國家自然科學(xué)基金。 在構(gòu)造逼近，球面t設(shè)計，反問題計算等領(lǐng)域取得了國際同行關(guān)注的結(jié)果，例如22年菲爾茲獎得主Mayna Viasovska就證明過安聰沛與和作者提出的關(guān)于球t-設(shè)計猜想。

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