A criterion for automatic image deconvolution with L₀‐norm regularization

Abstract

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.

Time-Dependent Image Restoration of Low-SNR Live-Cell Ca2 Fluorescence Microscopy Data

“…However, although motivated by demands of spatio-temporal imaging, the proposed formulation addressed only frame-by-frame deconvolution, i.e., the resulting algorithm was to be applied independently to each frame. While this is common to most image restoration methods (both deep learning and conventional approaches), recent work illustrated the benefits of taking the spatio- temporal nature of the acquired data into account [ 15 , 16 ].…”

Time-Dependent Image Restoration of Low-SNR Live Cell Ca2+ Fluorescence Microscopy Data

“…the resulting algorithm was to be applied independently to each frame. While this is common to most image restoration methods (both deep learning and conventional approaches), recent work illustrated benefits of taking into account the spatio-temporal nature of the acquired data [14,15].…”