Regularization Parameter Estimation for Non-Negative Hyperspectral Image Deconvolution

Abstract

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.

Online deconvolution for pushbroom hyperspectral imaging systems

“…Figure 3(c) corresponds to the Tikhonov approach with ℓ 2 spatial and spectral regularizers and Figure 3(d) corresponds to the non-negative version of the Tikhonov approach. The hyperparameters of the non-negative Tikhonov approach were estimated by the minimum distance criterion proposed in [25] and the same values were used for the standard Tikhonov approach. The results of the sequential deconvolution have almost the same resolution compared to both Tikhonov approaches.…”

Estimation of the Regularization Parameter of an On-Line NMF with Minimum Volume Constraint

“…Let S (K) µ and A (K) µ denote the estimated endmembers and abundances for a given value of µ. Following [16] the response curve (bi-objective case) is the linear plot of the data fitting versus minimum volume constraint cost for µ ∈ [0, +∞). The two objectives are respectively defined as:…”

“…Similarly to [1], this leads to a simple fixed point algorithm which also suffers from the same problems: hyperparameter range limitation, non-uniqueness of the maximal curvature. To overcome these two main drawbacks, it was proposed in [16] to estimate the hyperparameter by determining the MDC on response curve (bi-objective case) or response surface (multi-objective case) defined as the linear plot of the data fitting versus regularization cost. This paper aims at investigating the interest of such an approach for estimating the minimum volume hyperparameter of the on-line MVS-NMF.…”

“…This paper aims at investigating the interest of such an approach for estimating the minimum volume hyperparameter of the on-line MVS-NMF. Unlike [16] which applies the MDC to a deconvolution case with a Tikhonov regularization, the problem considered in this paper is the online source separation with minimum volume constraint, and presents different implementation problems, as explained in the following sections. The remainder of the paper is organized as follows: section 2 is briefly presenting the on-line MVS-NMF algorithm.…”

Spatio-Spectral Multichannel Reconstruction from few Low-Resolution Multispectral Data

“…Multichannel forward models have been proposed in [5], [6], where the system response is a block-diagonal matrix with circulant blocks. For instance, [7], [8], [9] address multichannel 2-D deconvolution problem for hyperspectral image deconvolution. They take into account the within-channel degradation, but not the between channel (or cross-channel) degradation.…”