This paper proposes a hyperspectral image deconvolution algorithm for the online restoration of hyperspectral images as provided by wiskbroom and pushbroom scanning systems. We introduce a least-mean-squares (LMS)-based framework accounting for the convolution kernel noncausality and including nonquadratic (zero attracting and piecewise constant) regularization terms. This results in the so-called sliding block regularized LMS (SBR-LMS), which maintains a linear complexity compatible with real-time processing in industrial applications. A model for the algorithm mean and mean-squares transient behavior is derived and the stability condition is studied. Experiments are conducted to assess the role of each hyper-parameter. A key feature of the proposed SBR-LMS is that it outperforms standard approaches in low SNR scenarios such as ultra-fast scanning.

This work aims at studying a method to automatically estimate regularization parameters of hyperspectral images 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) is proposed to estimate regularization parameters. It has good theoretical properties (uniqueness, robustness) from which a grid search based approach is proposed. It results in a fast approach to estimate the regularization parameters.

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.

We propose a sparse modal estimation approach for analyzing 2-D NMR signals. It consists in decomposing the 2-D problem into two 1-D modal estimations. Each 1-D problem is formulated in terms of simultaneous sparse approximation which is efficiently solved using the Simultaneous Orthogonal Matching Pursuit method associated with a multi-grid dictionary refinement. Then, we propose a new criterion for mode pairing which comes down to solve a sparse approximation problem involving a low dimensional dictionary. The effectiveness of the method is demonstrated on real NMR data.

This paper presents a methodology to estimate the parameters of two-dimensional damped/undamped exponentials from high complexity noisy signals, which is the case in 2-D nuclear magnetic resonance spectroscopy signals. The proposed approach performs adaptive subband decomposition combined with a classical frequency estimator based on the Prony model. At each node resulting from the decomposition tree, a stopping rule is computed in order to decide whether the decomposition must be continued or not. The rule is a flatness measure applied on residuals resulting from the estimation step. The method is demonstrated using a simulated signal.