arXiv subjects

Miguel Moscoso

Publications and source records attributed to Miguel Moscoso.

At least 19 recordsLinked to original sources

arXiv2026

Imaging with super-resolution in changing random media

We develop an imaging algorithm that exploits strong scattering to achieve super-resolution in changing random media. The method processes large and diverse array datasets using sparse dictionary learning, clustering, and multidimensional scaling. Starting from random initializations, the algorithm reliably extracts the unknown medium properties necessary for accurate imaging using back-propagation, $\ell_2$ or $\ell_1$ methods. Remarkably, scattering enhances resolution beyond homogeneous medium limits. When abundant data are available, the algorithm allows the realization of super-resolution in imaging.

physics.optics↗

arXiv2024

Super-resolution in disordered media using neural networks

We propose a methodology that exploits large and diverse data sets to accurately estimate the ambient medium's Green's functions in strongly scattering media. Given these estimates, obtained with and without the use of neural networks, excellent imaging results are achieved, with a resolution that is better than that of a homogeneous medium. This phenomenon, also known as super-resolution, occurs because the ambient scattering medium effectively enhances the physical imaging aperture. This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.

cs.LG↗

arXiv2023

Wave-informed dictionary learning for high-resolution imaging in complex media

We propose an approach for imaging in scattering media when large and diverse data sets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an unordered sensing matrix. The array data comes from many sparse sets of sources whose location and strength are not known to us. In the second step, the columns of the estimated sensing matrix are ordered for imaging using Multi-Dimensional Scaling with connectivity information derived from cross-correlations of its columns, as in time reversal. For these two steps to work together we need data from large arrays of receivers so the columns of the sensing matrix are incoherent for the first step, as well as from sub-arrays so that they are coherent enough to obtain the connectivity needed in the second step. Through simulation experiments, we show that the proposed approach is able to provide images in complex media whose resolution is that of a homogeneous medium.

cs.CV↗

arXiv2022

Quantitative phase and absorption contrast imaging

We present an algorithm for coherent diffractive imaging with phaseless measurements. It treats the forward model as a combination of coherent and incoherent waves. The algorithm reconstructs absorption and phase contrast that quantifies the attenuation and the refraction of the waves propagating through an object. It requires coherent or partially coherent illuminations, and several detectors to record the intensity of the distorted wave that passes through the object under inspection. The diversity of illuminations, obtained by putting masks between the source and the object, provides enough information for imaging. The computational cost of our algorithm is linear in the number of pixels of the image. Therefore, it is efficient for high-resolution imaging. Our algorithm guarantees exact recovery if the image is sparse for a given basis. Numerical experiments in the setting of phaseless diffraction imaging of sparse objects validate the efficiency and the precision of the suggested algorithm.

physics.comp-ph↗

arXiv2020

Fast signal recovery from quadratic measurements

We present a novel approach for recovering a sparse signal from cross-correlated data. Cross-correlations naturally arise in many fields of imaging, such as optics, holography and seismic interferometry. Compared to the sparse signal recovery problem that uses linear measurements, the unknown is now a matrix formed by the cross correlation of the unknown signal. Hence, the bottleneck for inversion is the number of unknowns that grows quadratically. The main idea of our proposed approach is to reduce the dimensionality of the problem by recovering only the diagonal of the unknown matrix, whose dimension grows linearly with the size of the problem. The keystone of the methodology is the use of an efficient {\em Noise Collector} that absorbs the data that come from the off-diagonal elements of the unknown matrix and that do not carry extra information about the support of the signal. This results in a linear problem whose cost is similar to the one that uses linear measurements. Our theory shows that the proposed approach provides exact support recovery when the data is not too noisy, and that there are no false positives for any level of noise. Moreover, our theory also demonstrates that when using cross-correlated data, the level of sparsity that can be recovered increases, scaling almost linearly with the number of data. The numerical experiments presented in the paper corroborate these findings.

eess.SP↗

arXiv2019

The Noise Collector for sparse recovery in high dimensions

The ability to detect sparse signals from noisy high-dimensional data is a top priority in modern science and engineering. A sparse solution of the linear system $A ρ= b_0$ can be found efficiently with an $l_1$-norm minimization approach if the data is noiseless. Detection of the signal's support from data corrupted by noise is still a challenging problem, especially if the level of noise must be estimated. We propose a new efficient approach that does not require any parameter estimation. We introduce the Noise Collector (NC) matrix $C$ and solve an augmented system $A ρ+ C η= b_0 + e$, where $ e$ is the noise. We show that the $l_1$-norm minimal solution of the augmented system has zero false discovery rate for any level of noise and with probability that tends to one as the dimension of $ b_0$ increases to infinity. We also obtain exact support recovery if the noise is not too large, and develop a Fast Noise Collector Algorithm which makes the computational cost of solving the augmented system comparable to that of the original one. Finally, we demonstrate the effectiveness of the method in applications to passive array imaging.

eess.SP↗

arXiv2019

Imaging with highly incomplete and corrupted data

We consider the problem of imaging sparse scenes from a few noisy data using an $l_1$-minimization approach. This problem can be cast as a linear system of the form $A \, ρ=b$, where $A$ is an $N\times K$ measurement matrix. We assume that the dimension of the unknown sparse vector $ρ\in {\mathbb{C}}^K$ is much larger than the dimension of the data vector $b \in {\mathbb{C}}^N$, i.e, $K \gg N$. We provide a theoretical framework that allows us to examine under what conditions the $\ell_1$-minimization problem admits a solution that is close to the exact one in the presence of noise. Our analysis shows that $l_1$-minimization is not robust for imaging with noisy data when high resolution is required. To improve the performance of $l_1$-minimization we propose to solve instead the augmented linear system $ [A \, | \, C] ρ=b$, where the $N \times Σ$ matrix $C$ is a noise collector. It is constructed so as its column vectors provide a frame on which the noise of the data, a vector of dimension $N$, can be well approximated. Theoretically, the dimension $Σ$ of the noise collector should be $e^N$ which would make its use not practical. However, our numerical results illustrate that robust results in the presence of noise can be obtained with a large enough number of columns $Σ\approx 10 K$.

eess.IV↗

arXiv2019

Synthetic aperture imaging with intensity-only data

We consider imaging the reflectivity of scatterers from intensity-only data recorded by a single moving transducer that both emits and receives signals, forming a synthetic aperture. By exploiting frequency illumination diversity, we obtain multiple intensity measurements at each location, from which we determine field cross-correlations using an appropriate phase controlled illumination strategy and the inner product polarization identity. The field cross-correlations obtained this way do not, however, provide all the missing phase information because they are determined up to a phase that depends on the receiver's location. The main result of this paper is an algorithm with which we recover the field cross-correlations up to a single phase that is common to all the data measured over the synthetic aperture, so all the data are synchronized. Thus, we can image coherently with data over all frequencies and measurement locations as if full phase information was recorded.

physics.comp-ph↗

arXiv2018

Robust multifrequency imaging with MUSIC

In this paper, we study the MUltiple SIgnal Classification (MUSIC) algorithm often used to image small targets when multiple measurement vectors are available. We show that this algorithm may be used when the imaging problem can be cast as a linear system that admits a special factorization. We discuss several active array imaging configurations where this factorization is exact, as well as other configurations where the factorization only holds approximately and, hence, the results provided by MUSIC deteriorate. We give special attention to the most general setting where an active array with an arbitrary number of transmitters and receivers uses signals of multiple frequencies to image the targets. This setting provides all the possible diversity of information that can be obtained from the illuminations. We give a theorem that shows that MUSIC is robust with respect to additive noise provided that the targets are well separated. The theorem also shows the relevance of using appropriate sets of controlled parameters, such as excitations, to form the images with MUSIC robustly. We present numerical experiments that support our theoretical results.

math.NA↗

arXiv2016

Multifrequency interferometric imaging with intensity-only measurements

We propose an illumination strategy for interferometric imaging that allows for robust depth recovery from intensity-only measurements. For an array with colocated sources and receivers, we show that all the possible interferometric data for multiple sources, receivers and frequencies can be recovered from intensity-only measurements provided that we have sufficient source location and frequency illumination diversity. There is no need for phase reconstruction in this approach. Using interferometric imaging methods we show that in homogeneous media there is no loss of resolution when imaging with intensities-only. If in these imaging methods we reduce incoherence by restricting the multifrequency interferometric data to nearby array elements and nearby frequencies we obtain robust images in weakly inhomogeneous background media with a somewhat reduced resolution.

math.OC↗

arXiv2016

Coherent imaging without phases

In this paper we consider narrow band, active array imaging of weak localized scatterers when only the intensities are recorded at an array with N transducers. We consider that the medium is homogeneous and, hence, wave propagation is fully coherent. This work is an extension of our previous paper, where we showed that using linear combinations of intensity-only measurements imaging of localized scatterers can be carried out efficiently using MUSIC or sparsity promoting optimization. Here we show the same strategy can be accomplished with only 3N-2 illuminations, therefore reducing enormously the data acquisition process. Furthermore, we show that in the paraxial regime one can form the images by using six illuminations only. In particular, this paraxial regime includes Fresnel and Fraunhofer diffraction. The key point of this work is that if one controls the illuminations, imaging with intensity-only can be easily reduced to a imaging with phases and, therefore, one can apply standard imaging techniques. Detailed numerical simulations illustrate the performance of the proposed imaging strategy with and without data noise.

math.OC↗

arXiv2016

Synthetic Aperture Imaging of Direction and Frequency Dependent Reflectivities

We introduce a synthetic aperture imaging framework that takes into consideration directional dependence of the reflectivity that is to be imaged, as well as its frequency dependence. We use an $\ell_1$ minimization approach that is coordinated with data segmentation so as to fuse information from multiple sub-apertures and frequency sub-bands. We analyze this approach from first principles and assess its performance with numerical simulations in an X-band radar regime.

math.OC↗

arXiv2015

Array imaging of localized objects in homogeneous and heterogeneous media

We present a comprehensive study of the resolution and stability properties of sparse promoting optimization theories applied to narrow band array imaging of localized scatterers. We consider homogeneous and heterogeneous media, and multiple and single scattering situations. When the media is homogeneous with strong multiple scattering between scatterers, we give a non-iterative formulation to find the locations and reflectivities of the scatterers from a nonlinear inverse problem in two steps, using either single or multiple illuminations. We further introduce an approach that uses the top singular vectors of the response matrix as optimal illuminations, which improves the robustness of sparse promoting optimization with respect to additive noise. When multiple scattering is negligible, the optimization problem becomes linear and can be reduced to a hybrid-$\ell_1$ method when optimal illuminations are used. When the media is random, and the interaction with the unknown inhomogeneities can be primarily modeled by wavefront distortions, we address the statistical stability of these methods. We analyze the fluctuations of the images obtained with the hybrid-$\ell_1$ method, and we show that it is stable with respect to different realizations of the random medium provided the imaging array is large enough. We compare the performance of the hybrid-$\ell_1$ method in random media to the widely used Kirchhoff migration and the multiple signal classification methods.

math.NA↗

arXiv2014

Illumination strategies for intensity-only imaging

We propose a new strategy for narrow band, active array imaging of localized scat- terers when only the intensities are recorded and measured at the array. We consider a homogeneous medium so that wave propagation is fully coherent. We show that imaging with intensity-only measurements can be carried out using the time reversal operator of the imaging system, which can be obtained from intensity measurements using an appropriate illumination strategy and the polarization identity. Once the time reversal operator has been obtained, we show that the images can be formed using its singular value decomposition (SVD). We use two SVD-based methods to image the scatterers. The proposed approach is simple and efficient. It does not need prior information about the sought image, and guarantees exact recovery in the noise-free case. Furthermore, it is robust with respect to additive noise. Detailed numerical simulations illustrate the performance of the proposed imaging strategy when only the intensities are captured.

math.OC↗

arXiv2013

Imaging strong localized scatterers with sparsity promoting optimization

We study active array imaging of small but strong scatterers in homogeneous media when multiple scattering between them is important. We use the Foldy-Lax equations to model wave propagation with multiple scattering when the scatterers are small relative to the wavelength. In active array imaging we seek to locate the positions and reflectivities of the scatterers, that is, to determine the support of the reflectivity vector and the values of its nonzero elements from echoes recorded on the array. This is a nonlinear inverse problem because of the multiple scattering. We show in this paper how to avoid the nonlinearity and form images non-iteratively through a two-step process which involves $\ell_1$ norm minimization. However, under certain illuminations imaging may be affected by screening, where some scatterers are obscured by multiple scattering. This problem can be mitigated by using multiple and diverse illuminations. In this case, we determine solution vectors that have a common support. The uniqueness and stability of the support of the reflectivity vector obtained with single or multiple illuminations are analyzed, showing that the errors are proportional to the amount of noise in the data with a proportionality factor dependent on the sparsity of the solution and the mutual coherence of the sensing matrix, which is determined by the geometry of the imaging array. Finally, to filter out noise and improve the resolution of the images, we propose an approach that combines optimal illuminations using the singular value decomposition of the response matrix together with sparsity promoting optimization jointly for all illuminations. This work is an extension of our previous paper [5] on imaging using optimization techniques where we now account for multiple scattering effects.

math-ph↗

arXiv2012

A differential equations approach to $l_1$-minimization with applications to array imaging

We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is independent of the relaxation parameter. An advantage of using the ordinary differential equations is that energy methods can be used to prove convergence. The connection to the discrete algorithms is provided by the Crandall-Liggett theory of monotone nonlinear semigroups. We illustrate the effectiveness of the discrete optimization algorithm in some sparse array imaging problems.

math.NA↗

arXiv1999

Current self-oscillations, spikes and crossover between charge monopole and dipole waves in semiconductor superlattices

Self-sustained current oscillations in weakly-coupled superlattices are studied by means of a self-consistent microscopic model of sequential tunneling including boundary conditions naturally. Well-to-well hopping and recycling of charge monopole domain walls produce current spikes (high frequency modulation) superimposed on the oscillation. For highly doped injecting contacts, the self-oscillations are due to dynamics of monopoles. As the contact doping decreases, a lower-frequency oscillatory mode due to recycling and motion of charge dipoles is predicted. For low contact doping, this mode dominates and monopole oscillations disappear. At intermediate doping, both oscillation modes coexist as stable solutions and hysteresis between them is possible.

cond-mat↗

arXiv1997

Microscopic Model for Sequential Tunneling in Semiconductor Multiple Quantum Wells

We propose a selfconsistent microscopic model of vertical sequential tunneling through a multi-quantum well.The model includes a detailed description of the contacts,uses the Transfer Hamiltonian for expressions of the current and it treats the Coulomb interaction within a mean field approximation. We analyze the current density through a double well and a superlattice and study the formation of electric field domains and multistability coming from the Coulomb interaction. Phase diagrams of parameter regions (bias, doping in the heterostructure and in the contacts,etc) where the different solutions exist are given.

cond-mat↗