Related papers: Statistical mechanics of image restoration and err…
Image registration is the inference of transformations relating noisy and distorted images. It is fundamental in computer vision, experimental physics, and medical imaging. Many algorithms and analyses exist for inferring shift, rotation,…
Denoising is omnipresent in image processing. It is usually addressed with algorithms relying on a set of hyperparameters that control the quality of the recovered image. Manual tuning of those parameters can be a daunting task, which calls…
We attempt image restoration in the framework of the Baysian inference. Recently, it has been shown that under a certain criterion the MAP (Maximum A Posterior) estimate, which corresponds to the minimization of energy, can be outperformed…
We present a surprisingly simple approach to high-accuracy calculations of critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in…
Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. We propose…
The AMIAS/RISE framework formulates emission tomography as a probabilistic inverse problem in which reconstructed images are sampled from a distribution defined by the measurement model and counting statistics. In this work we present a…
The surface code, one of the leading candidates for quantum error correction, is known to protect encoded quantum information against stochastic, i.e., incoherent errors. The protection against coherent errors, such as from unwanted gate…
A statistical learning/inference framework for color demosaicing is presented. We start with simplistic assumptions about color constancy, and recast color demosaicing as a blind linear inverse problem: color parameterizes the unknown…
In this paper, we extend the full replica symmetry breaking scheme to the Ising spin glass on a random regular graph. We propose a new martingale approach, that overcomes the limits of the Parisi-M\'ezard cavity method, providing a…
In this paper, we consider the problem of estimating the underlying graph associated with an Ising model given a number of independent and identically distributed samples. We adopt an \emph{approximate recovery} criterion that allows for a…
A new type of robust estimation problem is introduced where the goal is to recover a statistical model that has been corrupted after it has been estimated from data. Methods are proposed for "repairing" the model using only the design and…
The inherent noise in the observed (e.g., scanned) binary document image degrades the image quality and harms the compression ratio through breaking the pattern repentance and adding entropy to the document images. In this paper, we design…
We present in this article the use of probabilistic background constraints in astronomical image deconvolution to approach to a solution as an interval estimate. We elaborate our objective -- the interval estimate of the unknown object from…
Stein's unbiased risk estimator (SURE) has been shown to be an effective metric for determining optimal parameters for many applications. The topic of this article is focused on the use of SURE for determining parameters for blind…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these…
We propose a new fast algorithm for solving one of the standard formulations of frame-based image deconvolution: an unconstrained optimization problem, involving an $\ell_2$ data-fidelity term and a non-smooth regularizer. Our approach is…
Pixel-space full spectrum fitting exploiting non-linear $\chi^2$ minimization became a \emph{de facto} standard way of deriving internal kinematics from absorption line spectra of galaxies and star clusters. However, reliable estimation of…
The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be simply stated as follows. Given the…