Related papers: On Unbiased Parameter Estimation and Signal Recons…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. Our interest is in linear approaches to signal recovery, where "linear" means…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove…
The reconstruction of the unknown acoustic source is studied using the noisy multiple frequency data on a remote closed surface. Assume that the unknown source is coded in a spatial dependent piecewise constant function, whose support set…
A signal recovery problem is considered, where the same binary testing problem is posed over multiple, independent data streams. The goal is to identify all signals, i.e., streams where the alternative hypothesis is correct, and noises,…
We consider a wireless sensor network, sampling a bandlimited field, described by a limited number of harmonics. Sensor nodes are irregularly deployed over the area of interest or subject to random motion; in addition sensors measurements…
We consider the problem of pointwise estimation of multi-dimensional signals $s$, from noisy observations $(y_\tau)$ on the regular grid $\bZd$. Our focus is on the adaptive estimation in the case when the signal can be well recovered using…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
We propose a novel framework for joint magnetic resonance image reconstruction and uncertainty quantification using under-sampled k-space measurements. The problem is formulated as a Bayesian linear inverse problem, where prior…
In this paper, we consider the problem of recovering compressively sensed ultrasound images. We build on prior work, and consider a number of existing approaches that we consider to be the state-of-the-art. The methods we consider take…
We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible…
Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based…
The typical approach for recovery of spatially correlated signals is regularized least squares with a coupled regularization term. In the Bayesian framework, this algorithm is seen as a maximum-a-posterior estimator whose postulated prior…
Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance…
Consider a Gaussian memoryless multiple source with $m$ components with joint probability distribution known only to lie in a given class of distributions. A subset of $k \leq m$ components are sampled and compressed with the objective of…
In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate…
The paper analyses the possibility to recover different biomedical signals if limited number of samples is available. Having in mind that monitoring of health condition is done by measuring and observing key parameters such as heart…
Signal restoration and inverse problems are key elements in most real-world data science applications. In the past decades, with the emergence of machine learning methods, inversion of measurements has become a popular step in almost all…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…