Regularization Parameter Estimation for Non-Negative Hyperspectral Image Deconvolution

This paper aims at studying a method to automatically estimate the regularization parameters of non-negative hyperspectral image deconvolution methods. The deconvolution problem is formulated as a multi-objective optimization problem and the properties of the corresponding response surface are studied. Based on these properties, the minimum distance criterion (MDC) and the maximum curvature criterion (MCC) are proposed to estimate regularization parameters especially for the non-negativity constrained deconvolution problem. MDC has good theoretical properties (convexity and uniqueness) but requires to choose a reference point. On the contrary, MCC does not need to choose any reference point but does not have interesting theoretical properties. A grid-search-based approach to minimize the computational cost of MDC and MCC is proposed. It results in fast approaches to estimate the regularization parameters. Based on simulated 2D images, the proposed approaches are compared with the state-of-the-art methods, confirming the effectiveness of the MDC and MCC for the non-negativity constrained image deconvolution problem. In the case of non-negative hyperpsectral image deconvolution, the fast MDC yields better performances than the fast MCC. An application to real-world hyperspectral fluorescence microscopy images is also provided; it confirms the superiority of MDC.