L0范數(shù)平滑逼近的穩(wěn)健求解算法
doi: 10.11999/JEIT141590
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2.
(西安電子科技大學(xué)綜合業(yè)務(wù)網(wǎng)國家重點實驗室 西安 710071) ②(空軍工程大學(xué)航空航天工程學(xué)院 西安 710038)
基金項目:
國家自然科學(xué)基金(61379104)和陜西省自然科學(xué)基金(2014JM2- 6106)
Robust Computational Methods for Smoothed L0 Approximation
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2.
(State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China)
Funds:
The National Natural Science Foundation of China (61379104)
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摘要: 該文研究基于代理函數(shù)和先驗概率密度的L0范數(shù)平滑逼近問題的穩(wěn)健求解。首先，分析了平滑逼近函數(shù)的凹凸特性，給出提高恢復(fù)性能的參數(shù)調(diào)整策略與改進(jìn)的SL0和FOCUSS算法。其次，將噪聲背景下L0范數(shù)逼近過程進(jìn)行正則化表示，并基于牛頓方向推導(dǎo)其迭代重加權(quán)形式的求解框架，給出一種新的代理函數(shù)。最后，使用數(shù)值仿真證實了所提算法可以提高此類問題的求解的穩(wěn)健性，具有實用價值。
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關(guān)鍵詞:
- 非凸壓縮感知 /
- L0范數(shù)平滑逼近 /
- 迭代重加權(quán)算法
Abstract: Computational framework using surrogate functions and prior probability density functions, for smoothed L0 minimization approximation is studied in this paper, for the purpose of improving the recovery performance of non-convex compressed sensing. Firstly, a simple parameter adjusting strategy and modified SL0 and FOCUSS are presented, based on the convex-concave property analysis of approximation functions. Secondly, since L0 approximation problem can be viewed as a L0-Regularized Least Squares problem in noisy setting，a new computational framework called IRSL0 (Iteratively Reweighted SL0) is derived from the Newton direction, furthermore, a new surrogate function is also given. Finally, extensive numerical simulations demonstrate the robustness and applicability of the new theory and algorithms. -
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