论文标题
spoq $ \ ell_p $ -over- $ \ ell_q $正规化用于稀疏信号恢复应用于质谱
SPOQ $\ell_p$-Over-$\ell_q$ Regularization for Sparse Signal Recovery applied to Mass Spectrometry
论文作者
论文摘要
不确定的或不当的逆问题需要\ ldd {d}具有可拖动优化算法的声音解决方案的其他信息。稀疏性在此问题上产生了启发式方法，并在信号恢复，图像恢复或机器学习中进行了许多应用。由于$ \ ell_0 $计数度量几乎是无法处理的，因此许多统计或学习方法已投资于可计算代理，例如$ \ ell_1 $ norm。但是，后者并未表现出对稀疏数据的规模不变性的理想特性。我们提出了一个针对盲人反卷发的烟灰欧几里得/出租车$ \ ell_1 $ -over- $ \ ell_2 $ norm-ratio，我们建议SPOQ，这是一个平滑（大约）规模不变的惩罚功能的家族。它由$ \ ell_p $ -over- $ \ ell_q $ quasi-norm/norm比率的Lipschitz-差异性代理组成，$ p \ in \，] 0,2 [$ q \ q \ ge ge 2 $。该替代物嵌入了一种新颖的主要大小限制信任区域方法中，从而推广了可变的前向回溯算法。对于自然稀疏的质谱信号，我们表明SPOQ明显优于$ \ ell_0 $，$ \ ell_1 $，CAUCHY，WELSCH，SCAD，SCAD，SCAD和CELO对几种绩效措施的惩罚。还提供了有关SPOQ超参数调整的指南，提出了简单的数据驱动选择。
Underdetermined or ill-posed inverse problems require additional information for \ldd{d} sound solutions with tractable optimization algorithms. Sparsity yields consequent heuristics to that matter, with numerous applications in signal restoration, image recovery, or machine learning. Since the $\ell_0$ count measure is barely tractable, many statistical or learning approaches have invested in computable proxies, such as the $\ell_1$ norm. However, the latter does not exhibit the desirable property of scale invariance for sparse data. Extending the SOOT Euclidean/Taxicab $\ell_1$-over-$\ell_2$ norm-ratio initially introduced for blind deconvolution, we propose SPOQ, a family of smoothed (approximately) scale-invariant penalty functions. It consists of a Lipschitz-differentiable surrogate for $\ell_p$-over-$\ell_q$ quasi-norm/norm ratios with $p\in\,]0,2[$ and $q\ge 2$. This surrogate is embedded into a novel majorize-minimize trust-region approach, generalizing the variable metric forward-backward algorithm. For naturally sparse mass-spectrometry signals, we show that SPOQ significantly outperforms $\ell_0$, $\ell_1$, Cauchy, Welsch, SCAD and Celo penalties on several performance measures. Guidelines on SPOQ hyperparameters tuning are also provided, suggesting simple data-driven choices.
