Nonconvex Regularization in Remote Sensing

Abstract

In this paper, we study the effect of different regularizers and their implications in highdimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of regularization used and its parameterization.We consider regularization via traditional squared (!2) and sparsity-promoting (!1) norms, as well as more unconventional non convex regularizers (!p and log sum penalty). We compare their properties and advantages on several classification and linear unmoving tasks and provide advices on the choice of the best regularizer for the problemat hand. Finally,we also provide a fully functional toolbox for the community. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 Nonconvex Regularization in Remote SensingDevis Tuia, Senior Member, IEEE, Rémi Flamary, and Michel Barlaud, Senior Member, IEEE Abstract-In this paper, we study the effect of different regularizers and their implications in high-dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of regularization used and its parameterization. We consider regularization via traditional squared ( 2 ) and sparsity-promoting ( 1 ) norms, as well as more unconventional nonconvex regularizers ( p and log sum penalty). We compare their properties and advantages on several classification and linear unmixing tasks and provide advices on the choice of the best regularizer for the problem at hand. Finally, we also provide a fully functional toolbox for the community.

Detection and discrimination of various oil-contaminated soils using vegetation reflectance

“…The selected VI were finally tested to discriminate among treatments using L 2 -Regularized Logistic Regression (RLR), also known as Ridge regression (Friedman & Popescu 2004, Hoerl & Kennard 1970. RLR has been widely used for classification purposes in various domains including remote sensing (Tuia et al 2016, Zhang et al 2015, and revealed to be efficient when applied on vegetation (Erudel et al 2017). We only trained the RLR classifier at leaf scale to assess the robustness of VI at higher acquisition scales.…”

Hyperspectral Image Unmixing With Endmember Bundles and Group Sparsity Inducing Mixed Norms

“…This limits the applicability of proximal methods to solve this type of problems, and other types of algorithms (or of nonconvex sparsity inducing penalties) have been investigated in remote sensing (see e.g. [49] and references therein).…”

Spectral Unmixing with Sparsity and Structuring Constraints

“…While we acknowledge that imposing a lower value on a n may act as a sparse regularizer, in our experiments, however, the best 1 -norm-based solution was always found with a n 1, that is, the FCLS solution (1). The non-convex p,p<1 -norm regularization recently proposed in [10] may be more suited for enforcing sparsity, although optimization strategies in [10] also discard the sumto-one constraint. Standard greedy iterative algorithms [13] are also unadapted to cope with the sum-to-one constraint and with non-normalized dictionaries: since endmembers are reflectance spectra, the dictionary cannot be normalized without affecting the abundance estimation [12].…”

“…Cardinality constraints resort to combinatorial optimization. Sparse spectral unmixing has been proposed e.g., with 1 -norm [8,9] or p, p<1 -norm [10] regularization, or with a greedy Orthogonal Matching Pursuit procedure [9]. While computationally attractive, such approaches usually do not solve the original sparse problem, and they face difficulties in considering the sum-to-one constraint and nonnormalized dictionaries.…”