Related papers: Beyond consistent reconstructions: optimality and …
This paper is concerned with the problem of reconstructing an infinite-dimensional signal from a limited number of linear measurements. In particular, we show that for binary measurements (modelled with Walsh functions and Hadamard…
Subsampling is one of the popular methods to balance statistical efficiency and computational efficiency in the big data era. Most approaches aim at selecting informative or representative sample points to achieve good overall information…
Diffusion models have achieved remarkable progress in universal image restoration. While existing methods speed up inference by reducing sampling steps, substantial step intervals often introduce cumulative errors. Moreover, they struggle…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
Depth acquisition, based on active illumination, is essential for autonomous and robotic navigation. LiDARs (Light Detection And Ranging) with mechanical, fixed, sampling templates are commonly used in today's autonomous vehicles. An…
Random sampling has become a critical tool in solving massive matrix problems. For linear regression, a small, manageable set of data rows can be randomly selected to approximate a tall, skinny data matrix, improving processing time…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
We introduce a new method for the reconstruction of a function from linear measurements by means of oblique projections. The space spanned by the measurement vectors may be different from the subspace in which the function is reconstructed.…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
For a class $F$ of complex-valued functions on a set $D$, we denote by $g_n(F)$ its sampling numbers, i.e., the minimal worst-case error on $F$, measured in $L_2$, that can be achieved with a recovery algorithm based on $n$ function…
Learning-based and data-driven techniques have recently become a subject of primary interest in the field of reconstruction and regularization of inverse problems. Besides the development of novel methods, yielding excellent results in…
In today's modern era of Big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is sub-sampling, where a subset of the Big data is analysed and used as…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Deep generative models have become a standard for modeling priors for inverse problems, going beyond classical sparsity-based methods. However, existing theoretical guarantees are mostly confined to finite-dimensional vector spaces,…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…