Related papers: System Approximations and Generalized Measurements…
An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a…
Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients,…
Learning based methods are now ubiquitous for solving inverse problems, but their deployment in real-world applications is often hindered by the lack of ground truth references for training. Recent self-supervised learning strategies offer…
Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…
We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic…
This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…
This paper is concerned with function reconstruction from samples. The sampling points used in several approaches are (1) structured points connected with fast algorithms or (2) unstructured points coming from, e.g., an initial random draw…
Network reconstruction is important to the understanding and control of collective dynamics in complex systems. Most real networks exhibit sparsely connected properties, and the connection parameter is a signal (0 or 1). Well-known…
The surge of massive antenna arrays in wireless networks calls for the adoption of analog/hybrid array solutions, where multiple antenna elements are driven by a common radio front end to form a beam along a specific angle in order to…
In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a…
Graph-based methods have been quite successful in solving unsupervised and semi-supervised learning problems, as they provide a means to capture the underlying geometry of the dataset. It is often desirable for the constructed graph to…
An accurate treatment of electronic spectra in large systems with a technique such as time dependent density functional theory (TDDFT) is computationally challenging. Due to the Nyquist sampling theorem, direct real time simulations must be…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
Instead of sampling a function at a single point, average sampling takes the weighted sum of function values around the point. Such a sampling strategy is more practical and more stable. In this note, we present an explicit method with an…
In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram)…
Measurement data is often sampled irregularly i.e. not on equidistant time grids. This is also true for Hamiltonian systems. However, existing machine learning methods, which learn symplectic integrators, such as SympNets [20] and…
Adaptive experiments are becoming increasingly popular in real-world applications for effectively maximizing in-sample welfare and efficiency by data-driven sampling. Despite their growing prevalence, however, the statistical foundations…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
We derive a compressive sampling method for acoustic field reconstruction using field measurements on a predefined spherical grid that has theoretically guaranteed relations between signal sparsity, measurement number, and reconstruction…