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

The design, construction, and commissioning of the KATRIN experiment

The KArlsruhe TRItium Neutrino (KATRIN) experiment, which aims to make a direct and model-independent determination of the absolute neutrino mass scale, is a complex experiment with many components. More than 15 years ago, we published a technical design report (TDR) [1] to describe the hardware design and requirements to achieve our sensitivity goal of 0.2 eV at 90% C.L. on the neutrino mass. Since then there has been considerable progress, culminating in the publication of first neutrino mass results with the entire beamline operating [2]. In this paper, we document the current state of all completed beamline components (as of the first neutrino mass measurement campaign), demonstrate our ability to reliably and stably control them over long times, and present details on their respective commissioning campaigns

A spatially explicit model for density that accounts for availability: a case study with Mojave desert tortoises

Estimating population density and identifying those areas where density is changing through time are central to prioritizing conservation and management strategies. Obtaining reliable estimates of density and trends can be challenging, however, especially for long-lived species that are rare, have broad geographic distributions, and are difficult to detect reliably during field surveys. We developed a hierarchical model for distance-sampling data that characterizes spatial variation in density at two scales and simultaneously estimates regional trends while accounting for variation in detection probability and availability across surveys. We applied the model to data collected over a 20-year period (2001–2020) in an area that encompassed most of the geographic range of the Mojave desert tortoise (Gopherus agassizii). Density of adult tortoises varied with multiple biotic and abiotic features, including topography, aspect, geology, and seasonal precipitation and temperature regimes. Across the entire period and study area, the density of adult tortoises decreased by an average of 1.8% per year (95% CI = −3.5% to −0.2%). Trends varied geographically, however, with the steepest declines in the western part of the range (−4.1%, −6.9% to −1.3%). Accounting for habitat loss across our study area, the abundance of this threatened species declined by an estimated 129,000 adults (36%) between 2001 and 2020. Our modeling approach extends traditional distance-sampling frameworks by accounting for ecological and observational processes that could mask spatiotemporal variation in density and, at the same time, provides spatially explicit estimates to guide conservation and management strategies for tortoises and other rare species. © 2023 The Authors. Ecosphere published by Wiley Periodicals LLC on behalf of The Ecological Society of America.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Production of a spin-polarized, metastable He(23 S) beam for studies in atomic and surface physics

Baum G, Raith W, Steidl H. Production of a spin-polarized, metastable He(23 S) beam for studies in atomic and surface physics. Z.Phys. D. 1988;10(2-3):171-178.This beam was developed as a target for a crossed-beam electron-atom scattering experiment on the interaction of a polarized spin-1/2 electron with a polarized spin-1 atom. In the future this beam will be used in "Spin-Polarized Metastable Atom Deexcitation Spectroscopy" (SPMDS) for studying ferromagnetic surfaces without and with adsorbate layers. We use a discharge source for producing a beam of metastable helium atoms, a permanent sextupole magnet with a central stop at its exit for selecting He(2^3 S) atoms in the Zeeman substate ms=+1, a zero-field spin flipper for reversing the atomic beam polarization with respect to a magnetic guiding field, and a Stern-Gerlach magnet for analyzing the atomic polarization. At a distance of 90 cm beyond the exit of the sextupole, in the "interaction region" of an experiment, the polarized beam has a circular cross section of about 6 mm FWHM and a particle density of 1·10^7 atoms/cm^3. The reversible spin polarization was determined asP=0.90±0.02. A possible contamination of the beam with metastable singlet atoms is included within this value; the ground-state He atoms are not considered to be part of the polarized beam. An observed contamination with long-lived Rydberg atoms can easily be destroyed by applying a high electric field

Power of monitoring programmes to detect decline and recovery of rare and vulnerable fish

1. Abundance trends provide key guidance when setting conservation priorities, whether indicating population decline, stability or recovery. Knowledge of the power of surveys to detect trends is essential, as the consequences of not detecting a real trend can be profound. 2. Unfortunately, some surveys have been established with no assessment of power, and others are used to study species that were not their original focus. The latter is common in the marine environment, where rare fish are monitored using catch data from surveys that target more abundant commercially fished species. 3. We calculated the power of a large-scale annual monitoring survey (the English North Sea bottom trawl survey) to detect decline and recovery of species that are vulnerable to fishing. As fisheries exploitation invariably precedes scientific investigation, the survey began after many vulnerable species had already been depleted. 4. The power of the survey to detect declines in the abundance of vulnerable species on time scales of < 10 years was low and the survey often failed to detect declines that would lead to listings under the IUCN A1 Red List criteria. Thus conservation prioritization based solely on survey data may fail to identify species at risk of regional extinction. 5. If conservation measures were effective, and vulnerable populations recovered at the maximum potential rate, 5-10 years of monitoring would often be required to detect recovery. 6. Power to detect trends in abundance was increased by developing a composite indicator that reflected trends in abundance of several vulnerable species. This indicator provided an overview of their conservation status. 7. Synthesis and applications. Consistent with the precautionary principle, conservation prioritization and management action should not depend on the statistical significance of recent abundance trends when low power is a consequence of historical depletion. If the conservation prioritization and management of rare and/or vulnerable species have to be predicated on evidence of significant declines, then higher type 1 error rates (falsely detecting a decline) should be acceptable. This is because the costs of type 1 errors are lower than those of type 2 (failure to detect a real decline)

Effect of human activities on the behaviour of breeding Spanish imperial eagles (Aquila adalberti): management implications for the conservation of a threatened species

We studied (14 500 h of field observations during 20 breeding attempts by 10 pairs) the effects of human activities on the behaviour of breeding Spanish imperial eagles. The probability that human activities around nest sites provoked a flight reaction varied significantly among territories and among types of activity, and increased when the distance between the activity and the nest site decreased, and increased when the number of people involved in each intrusion was higher. Pedestrian activities (mainly by hunters, campers and ecotourists) caused more flight reactions than vehicles. Overall, the probability of a reaction increased sharply when activities occurred at less than 450 m from the nest, but was negligible if they occurred at 800 m. Reaction probability was lower in territories with higher intrusion frequencies (which suggests that some habituation occurs), where the nest was not visible from the tracks, and in less ‘plain’ or ‘accessible’ territories. Hatching rate was affected negatively by the frequency of human activities. Our results suggest that the critical inner buffer zone around Spanish imperial eagle nests should be established at a minimum radius of 500 m, and the vulnerable zones at a minimum of 800 m, bearing in mind the physiography of the terrain and the visibility of the nests. Finally, in future studies of nest-site selection with this species, it would be advisable to use a variable that quantifies (through field observations) human disturbance frequenc