Related papers: Optimal Adaptive Nonparametric Denoising of Multid…
In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to…
A critical task in graph signal processing is to estimate the true signal from noisy observations over a subset of nodes, also known as the reconstruction problem. In this paper, we propose a node-adaptive regularization for graph signal…
One-class anomaly detection aims to detect objects that do not belong to a predefined normal class. In practice training data lack those anomalous samples; hence state-of-the-art methods are trained to discriminate between normal and…
Signal decomposition is a classical problem in signal processing, which aims to separate an observed signal into two or more components each with its own property. Usually each component is described by its own subspace or dictionary.…
We focus on a multidimensional field with uncorrelated spectrum, and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes…
Based on the principles of information theory, measure theory, and theoretical computer science, we introduce a signal deconvolution method with a wide range of applications to coding theory, particularly in zero-knowledge one-way…
As in standard linear regression, in truncated linear regression, we are given access to observations $(A_i, y_i)_i$ whose dependent variable equals $y_i= A_i^{\rm T} \cdot x^* + \eta_i$, where $x^*$ is some fixed unknown vector of interest…
Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have…
We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the…
We consider the problem of reconstructing a signal from multi-layered (possibly) non-linear measurements. Using non-rigorous but standard methods from statistical physics we present the Multi-Layer Approximate Message Passing (ML-AMP)…
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian,…
Likelihood-free inference is quickly emerging as a powerful tool to perform fast/effective parameter estimation. We demonstrate a technique of optimizing likelihood-free inference to make it even faster by marginalizing symmetries in a…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
We consider nonparametric inference of finite dimensional, potentially non-pathwise differentiable target parameters. In a nonparametric model, some examples of such parameters that are always non pathwise differentiable target parameters…
Recovering a low-rank signal matrix from its noisy observation, commonly known as matrix denoising, is a fundamental inverse problem in statistical signal processing. Matrix denoising methods are generally based on shrinkage or thresholding…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…
In order to improve the least mean squares (LMS) adaptation algorithm to accommodate the nonlinear transfer function, and to adjust the coefficients of adaptive filter during the actual implement of bias voltage and signal amplitude,…