Automatic penalty adjustment in sparse deconvolution with penalized least squares is required for improved reliability and broader applicability. In sparse deconvolution with an L0‐norm penalty, the latent signal is by nature discontinuous, and the magnitudes of the residuals and sparsity regularization terms are of different order of magnitude. This makes approaches such as generalized cross validation or L‐curve unsuitable in practice. The criterion proposed in this paper is based on the representation of the sum of the normalized residuals and regularization terms (SNT) as a function of the penalty parameter. We observed that the minimum of the SNT corresponds to the optimal value of the penalty parameter. This approach was tested in the context of super‐resolution fluorescence microscopy imaging. Both simulated and real live‐cell images characterized by different complexities and emitter densities were analyzed to assess the performance of the developed optimization strategy and to demonstrate its usefulness over manual tuning.

中文翻译：

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具有 L 0 范数正则化的自动图像反卷积标准

为了提高可靠性和更广泛的适用性，需要在带有惩罚最小二乘法的稀疏反卷积中进行自动惩罚调整。在具有 L0 范数惩罚的稀疏反卷积中，潜在信号本质上是不连续的，残差和稀疏正则化项的大小具有不同的数量级。这使得广义交叉验证或 L 曲线等方法在实践中不适用。本文提出的标准基于归一化残差和正则化项 (SNT) 之和作为惩罚参数的函数的表示。我们观察到 SNT 的最小值对应于惩罚参数的最佳值。这种方法在超分辨率荧光显微镜成像的背景下进行了测试。