254 research outputs found
Image reconstruction in optical interferometry: Benchmarking the regularization
With the advent of infrared long-baseline interferometers with more than two
telescopes, both the size and the completeness of interferometric data sets
have significantly increased, allowing images based on models with no a priori
assumptions to be reconstructed. Our main objective is to analyze the multiple
parameters of the image reconstruction process with particular attention to the
regularization term and the study of their behavior in different situations.
The secondary goal is to derive practical rules for the users. Using the
Multi-aperture image Reconstruction Algorithm (MiRA), we performed multiple
systematic tests, analyzing 11 regularization terms commonly used. The tests
are made on different astrophysical objects, different (u,v) plane coverages
and several signal-to-noise ratios to determine the minimal configuration
needed to reconstruct an image. We establish a methodology and we introduce the
mean-square errors (MSE) to discuss the results. From the ~24000 simulations
performed for the benchmarking of image reconstruction with MiRA, we are able
to classify the different regularizations in the context of the observations.
We find typical values of the regularization weight. A minimal (u,v) coverage
is required to reconstruct an acceptable image, whereas no limits are found for
the studied values of the signal-to-noise ratio. We also show that
super-resolution can be achieved with increasing performance with the (u,v)
coverage filling. Using image reconstruction with a sufficient (u,v) coverage
is shown to be reliable. The choice of the main parameters of the
reconstruction is tightly constrained. We recommend that efforts to develop
interferometric infrastructures should first concentrate on the number of
telescopes to combine, and secondly on improving the accuracy and sensitivity
of the arrays.Comment: 15 pages, 16 figures; accepted in A&
Generalized Forward-Backward Splitting
This paper introduces the generalized forward-backward splitting algorithm
for minimizing convex functions of the form , where
has a Lipschitz-continuous gradient and the 's are simple in the sense
that their Moreau proximity operators are easy to compute. While the
forward-backward algorithm cannot deal with more than non-smooth
function, our method generalizes it to the case of arbitrary . Our method
makes an explicit use of the regularity of in the forward step, and the
proximity operators of the 's are applied in parallel in the backward
step. This allows the generalized forward backward to efficiently address an
important class of convex problems. We prove its convergence in infinite
dimension, and its robustness to errors on the computation of the proximity
operators and of the gradient of . Examples on inverse problems in imaging
demonstrate the advantage of the proposed methods in comparison to other
splitting algorithms.Comment: 24 pages, 4 figure
Non-convex regularization in remote sensing
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 parametrization. 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.Comment: 11 pages, 11 figure
Vast volatility matrix estimation for high-frequency financial data
High-frequency data observed on the prices of financial assets are commonly
modeled by diffusion processes with micro-structure noise, and realized
volatility-based methods are often used to estimate integrated volatility. For
problems involving a large number of assets, the estimation objects we face are
volatility matrices of large size. The existing volatility estimators work well
for a small number of assets but perform poorly when the number of assets is
very large. In fact, they are inconsistent when both the number, , of the
assets and the average sample size, , of the price data on the assets go
to infinity. This paper proposes a new type of estimators for the integrated
volatility matrix and establishes asymptotic theory for the proposed estimators
in the framework that allows both and to approach to infinity. The
theory shows that the proposed estimators achieve high convergence rates under
a sparsity assumption on the integrated volatility matrix. The numerical
studies demonstrate that the proposed estimators perform well for large and
complex price and volatility models. The proposed method is applied to real
high-frequency financial data.Comment: Published in at http://dx.doi.org/10.1214/09-AOS730 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Improvement of image quality of time-domain diffuse optical tomography with lp sparsity regularization
An lp (0 < p ≤ 1) sparsity regularization is applied to time-domain diffuse optical tomography with a gradient-based nonlinear optimization scheme to improve the spatial resolution and the robustness to noise. The expression of the lp sparsity regularization is reformulated as a differentiable function of a parameter to avoid the difficulty in calculating its gradient in the optimization process. The regularization parameter is selected by the L-curve method. Numerical experiments show that the lp sparsity regularization improves the spatial resolution and recovers the difference in the absorption coefficients between two targets, although a target with a small absorption coefficient may disappear due to the strong effect of the lp sparsity regularization when the value of p is too small. The lp sparsity regularization with small p values strongly localizes the target, and the reconstructed region of the target becomes smaller as the value of p decreases. A phantom experiment validates the numerical simulations
Non-line-of-sight reconstruction via structure sparsity regularization
Non-line-of-sight (NLOS) imaging allows for the imaging of objects around a
corner, which enables potential applications in various fields such as
autonomous driving, robotic vision, medical imaging, security monitoring, etc.
However, the quality of reconstruction is challenged by low signal-noise-ratio
(SNR) measurements. In this study, we present a regularization method, referred
to as structure sparsity (SS) regularization, for denoising in NLOS
reconstruction. By exploiting the prior knowledge of structure sparseness, we
incorporate nuclear norm penalization into the cost function of directional
light-cone transform (DLCT) model for NLOS imaging system. This incorporation
effectively integrates the neighborhood information associated with the
directional albedo, thereby facilitating the denoising process. Subsequently,
the reconstruction is achieved by optimizing a directional albedo model with SS
regularization using fast iterative shrinkage-thresholding algorithm. Notably,
the robust reconstruction of occluded objects is observed. Through
comprehensive evaluations conducted on both synthetic and experimental
datasets, we demonstrate that the proposed approach yields high-quality
reconstructions, surpassing the state-of-the-art reconstruction algorithms,
especially in scenarios involving short exposure and low SNR measurements.Comment: 8 pages, 5 figure
A fast patch-dictionary method for whole image recovery
Various algorithms have been proposed for dictionary learning. Among those
for image processing, many use image patches to form dictionaries. This paper
focuses on whole-image recovery from corrupted linear measurements. We address
the open issue of representing an image by overlapping patches: the overlapping
leads to an excessive number of dictionary coefficients to determine. With very
few exceptions, this issue has limited the applications of image-patch methods
to the local kind of tasks such as denoising, inpainting, cartoon-texture
decomposition, super-resolution, and image deblurring, for which one can
process a few patches at a time. Our focus is global imaging tasks such as
compressive sensing and medical image recovery, where the whole image is
encoded together, making it either impossible or very ineffective to update a
few patches at a time.
Our strategy is to divide the sparse recovery into multiple subproblems, each
of which handles a subset of non-overlapping patches, and then the results of
the subproblems are averaged to yield the final recovery. This simple strategy
is surprisingly effective in terms of both quality and speed. In addition, we
accelerate computation of the learned dictionary by applying a recent block
proximal-gradient method, which not only has a lower per-iteration complexity
but also takes fewer iterations to converge, compared to the current
state-of-the-art. We also establish that our algorithm globally converges to a
stationary point. Numerical results on synthetic data demonstrate that our
algorithm can recover a more faithful dictionary than two state-of-the-art
methods.
Combining our whole-image recovery and dictionary-learning methods, we
numerically simulate image inpainting, compressive sensing recovery, and
deblurring. Our recovery is more faithful than those of a total variation
method and a method based on overlapping patches
Multi-scale Mining of fMRI data with Hierarchical Structured Sparsity
International audienceInverse inference, or "brain reading", is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data, based on pattern recognition and statistical learning. By predicting some cognitive variables related to brain activation maps, this approach aims at decoding brain activity. Inverse inference takes into account the multivariate information between voxels and is currently the only way to assess how precisely some cognitive information is encoded by the activity of neural populations within the whole brain. However, it relies on a prediction function that is plagued by the curse of dimensionality, since there are far more features than samples, i.e., more voxels than fMRI volumes. To address this problem, different methods have been proposed, such as, among others, univariate feature selection, feature agglomeration and regularization techniques. In this paper, we consider a sparse hierarchical structured regularization. Specifically, the penalization we use is constructed from a tree that is obtained by spatially-constrained agglomerative clustering. This approach encodes the spatial structure of the data at different scales into the regularization, which makes the overall prediction procedure more robust to inter-subject variability. The regularization used induces the selection of spatially coherent predictive brain regions simultaneously at different scales. We test our algorithm on real data acquired to study the mental representation of objects, and we show that the proposed algorithm not only delineates meaningful brain regions but yields as well better prediction accuracy than reference methods
Non-line-of-sight imaging with arbitrary illumination and detection pattern
Non-line-of-sight (NLOS) imaging aims at reconstructing targets obscured from
the direct line of sight. Existing NLOS imaging algorithms require dense
measurements at rectangular grid points in a large area of the relay surface,
which severely hinders their availability to variable relay scenarios in
practical applications such as robotic vision, autonomous driving, rescue
operations and remote sensing. In this work, we propose a Bayesian framework
for NLOS imaging with no specific requirements on the spatial pattern of
illumination and detection points. By introducing virtual confocal signals, we
design a confocal complemented signal-object collaborative regularization
(CC-SOCR) algorithm for high quality reconstructions. Our approach is capable
of reconstructing both albedo and surface normal of the hidden objects with
fine details under the most general relay setting. Moreover, with a regular
relay surface, coarse rather than dense measurements are enough for our
approach such that the acquisition time can be reduced significantly. As
demonstrated in multiple experiments, the new framework substantially enhances
the applicability of NLOS imaging.Comment: main article: 32 pages with 8 figures; supplementary information: 49
pages with 26 figure
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