CLEAR: Covariant LEAst-square Re-fitting with applications to image restoration

In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a "twicing" flavor and allows re-fitting the restored signal by adding back a local affine transformation of the residual term. We illustrate the benefits of our method on numerical simulations for image restoration tasks

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Growers’ risk perception and trust in control options for huanglongbing citrus-disease in Florida and California

Citrus huanglongbing disease is an acute bacterial disease that threatens the sustainability of citrus production across the world. In the USA, the Asian Citrus Psyllid (ACP) is responsible for spreading the disease. Successful suppression of HLB requires action against ACP at large spatial scales, i.e. growers must cooperate. In Florida and California, the regions in which citrus is grown have been split into management areas and growers are encouraged to coordinate spraying of insecticide across these (area-wide control). We surveyed growers from Florida and California to assess the consensus of opinions concerning issues that influence HLB management. Our results show that risk perception and trust in control options are central to the decision by growers on whether to join an area-wide control program. Growers’ perceptions on risk and control efficacy are influenced by information networks and observations about the state of the epidemic and psyllid populations. Researchers and extension agents were reported to have the largest influence on these perceptions. Differences in opinion between California and Florida growers as to the efficacy of treatments were largely a function of experience. A large proportion of growers identified failure of participation as a reason why participation in area-wide control might not occur

The exploitation of the non local paradigm for sar 3d reconstruction

In the last decades, several approaches for solving the Phase Unwrapping (PhU) problem using multi-channel Interferometric Synthetic Aperture Radar (InSAR) data have been developed. Many of the proposed approaches are based on statistical estimation theory, both classical and Bayesian. In particular, the statistical approaches based on the use of the whole complex multi-channel dataset have turned to be effective. The latter are based on the exploitation of the covariance matrix, which contains the parameters of interest. In this paper, the added value of the Non Local (NL) paradigm within the InSAR multi-channel PhU framework is investigated. The analysis of the impact of NL technique is performed using multi-channel realistic simulated data and X-band data