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When inverting solar spectra, image degradation effects that are present in the data are usually approximated or not considered. We develop a data reduction method that takes these issues into account and minimizes the resulting errors. By…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
Regularization methods improve the stability of ill-posed inverse problems by introducing some a priori characteristics for the solution such as smoothness or sharpness. In this contribution, we propose a multidimensional, scale-dependent…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
We investigate the cross-calibration of the Hinode/SOT-SP and SDO/HMI instrument meta-data, specifically the correspondence of the scaling and pointing information. Accurate calibration of these datasets gives the correspondence needed by…
An optimal estimation inverse method is presented which can be used to retrieve simultaneously vertical profiles of temperature and specific humidity, in addition to surface pressure, from satellite-to-satellite radio occultation…
We present an adaptive regularization scheme for optimizing composite energy functionals arising in image analysis problems. The scheme automatically trades off data fidelity and regularization depending on the current data fit during the…
We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in…
Inverse problems are often ill-posed, with solutions that depend sensitively on data. In any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is…
Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…
We present new constraints on the high-temperature emission measure of a non-flaring solar active region using observations from the recently flown Focusing Optics X-ray Solar Imager sounding rocket payload. FOXSI has performed the first…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Implicit inverse problems, in which noisy observations of a physical quantity are used to infer a nonlinear functional applied to an associated function, are inherently ill posed and often exhibit non uniqueness of solutions. Such problems…
Continuum emission from a solar flare observed with the Extreme ultraviolet Imaging Spectrometer (EIS) on board the Hinode satellite is used to obtain the radiometric calibration of the instrument. The flare had a GOES class of M8, and…
Regularization is necessary for solving nonlinear ill-posed inverse problems arising in different fields of geosciences. The base of a suitable regularization is the prior expressed by the regularizer, which can be non-adaptive or adaptive…
We propose a regularization method to solve a nonlinear ill-posed problem connected to inversion of data gathered by a ground conductivity meter.
We propose and test improvements to state-of-the-art techniques of Bayeasian statistical inference based on pseudolikelihood maximization with $\ell_1$ regularization and with decimation. In particular, we present a method to determine the…
Dense depth and surface normal predictors should possess the equivariant property to cropping-and-resizing -- cropping the input image should result in cropping the same output image. However, we find that state-of-the-art depth and normal…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
In genetical genomics studies, it is important to jointly analyze gene expression data and genetic variants in exploring their associations with complex traits, where the dimensionality of gene expressions and genetic variants can both be…