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.

deconvolution, image, optimization, regularization parameter, sparsity,
Journal of Chemometrics
Department of Biostatistics

Ahmad, M. (Mohamad), Hugelier, S. (Siewert), Vitale, R. (Raffaele), Eilers, P.H.C, & Ruckebusch, C. (2020). A criterion for automatic image deconvolution with L0-norm regularization. Journal of Chemometrics. doi:10.1002/cem.3227