Related papers: Algebraic signal sampling, Gibbs phenomenon and Pr…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…
We consider the reconstruction of spike train signals of the form $$F(x) = \sum_{i=1}^d a_i \delta(x-x_i),$$ from their moments measurements $m_k(F)=\int x^k F(x) dx = \sum_{i=1}^d a_ix^k$. When some of the nodes $x_i$ near collide the…
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…
We develop a method to infer log-normal random fields from measurement data affected by Gaussian noise. The log-normal model is well suited to describe strictly positive signals with fluctuations whose amplitude varies over several orders…
Due to excessive need for faster propagations of signals and necessity to reduce number of measurements and rapidly increase efficiency, new sensing theories have been proposed. Conventional sampling approaches that follow Shannon-Nyquist…
Many statistical problems include model parameters that are defined as the solutions to optimization sub-problems. These include classical approaches such as profile likelihood as well as modern applications involving flow networks or…
We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…
Gibbs-type exchangeable random partitions, which is a class of multiplicative measures on the set of positive integer partitions, appear in various contexts, including Bayesian statistics, random combinatorial structures, and stochastic…
We consider time-dependent dynamical systems arising as sequential compositions of self-maps of a probability space. We establish conditions under which the Birkhoff sums for multivariate observations, given a centering and a general…
Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…
In this paper, the problem of reconstruction of signals in mixed Lebesgue spaces from their random average samples has been studied. Probabilistic sampling inequalities for certain subsets of shift-invariant spaces have been derived. It is…
We investigate the problem of reconstructing a 2D piecewise smooth function from its bandlimited Fourier measurements. This is a well known and well studied problem with many real world implications, in particular in medical imaging. While…
With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
We apply a new numerical method, the singular Fourier-Pad\'e (SFP) method invented by Driscoll and Fornberg (2001, 2011), to price European-type options in L\'evy and affine processes. The motivation behind this application is to reduce the…
Many inverse problems arising in applications come from continuum models where the unknown parameter is a field. In practice the unknown field is discretized resulting in a problem in $\mathbb{R}^N$, with an understanding that refining the…
Gibbs-type random probability measures, or Gibbs-type priors, are arguably the most "natural" generalization of the celebrated Dirichlet prior. Among them the two parameter Poisson-Dirichlet prior certainly stands out for the mathematical…
The Gibbs phenomenon is widely known for Fourier expansions of periodic functions and refers to the phenomenon that the $n$th Fourier partial sums overshoot a target function at jump discontinuities in such a way that such overshoots do not…
In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…
Suppose that $\ff \in \reals^{n}$ is a vector of $n$ error-contaminated measurements of $n$ smooth values measured at distinct and strictly ascending abscissae. The following projective technique is proposed for obtaining a vector of smooth…