Related papers: Generalized SURE for Exponential Families: Applica…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
1. Parameter inference from distorted measurements is discussed. 2. Smeared measurements are unfolded without explicit regularization. The corresponding results are unbiased and permit to fit parameters and to apply quantitative…
We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably…
This paper proposes methods for producing compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters $\mu_ {1:n}$ and known $\sigma_{1:n}$ with observations $Y_i \sim \textsf{N}(\mu_i, \sigma_i^2)$, the…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…
The proposed smooth blockwise iterative thresholding estimator (SBITE) is a model selection technique defined as a fixed point reached by iterating a likelihood gradient-based thresholding function. The smooth James-Stein thresholding…
There are two major routes to address the ubiquitous family of inverse problems appearing in signal and image processing, such as denoising or deblurring. A first route relies on Bayesian modeling, where prior probabilities are used to…
Diffusion models have recently gained popularity for accelerated MRI reconstruction due to their high sample quality. They can effectively serve as rich data priors while incorporating the forward model flexibly at inference time, and they…
Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem,…
Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc.…
Our goal is to develop a general strategy to decompose a random variable $X$ into multiple independent random variables, without sacrificing any information about unknown parameters. A recent paper showed that for some well-known natural…
The James-Stein (JS) shrinkage estimator is a biased estimator that captures the mean of Gaussian random vectors.While it has a desirable statistical property of dominance over the maximum likelihood estimator (MLE) in terms of mean squared…
When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…
Modern computational models in supervised machine learning are often highly parameterized universal approximators. As such, the value of the parameters is unimportant, and only the out of sample performance is considered. On the other hand…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…
In this paper, we propose an interpretable denoising method for graph signals using regularization by denoising (RED). RED is a technique developed for image restoration that uses an efficient (and sometimes black-box) denoiser in the…
We consider quasi-admissibility/inadmissibility of Stein-type shrinkage estimators of the mean of a multivariate normal distribution with covariance matrix an unknown multiple of the identity. Quasi-admissibility/inadmissibility is defined…
Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, LSSC. In the past, convex optimization…