Related papers: Towards optimal sensor placement for inverse probl…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
This paper considers the linear inverse problem where we wish to estimate a structured signal $x$ from its corrupted observations. When the problem is ill-posed, it is natural to make use of a convex function $f(\cdot)$ that exploits the…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
This paper proposes a systematic mathematical analysis of both the direct and inverse acoustic scattering problem given the source in Radon measure space. For the direct problem, we investigate the well-posedness including the existence,…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
This paper considers the inverse problem of identifying the source term of parabolic equations from sparse boundary measurements. We used data from moving sensors to locate the unknown source term. This work first proves the uniqueness of…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We consider the problem of recovering an unknown effectively $(s_1,s_2)$-sparse low-rank-$R$ matrix $X$ with possibly non-orthogonal rank-$1$ decomposition from incomplete and inaccurate linear measurements of the form $y = \mathcal A (X) +…
It is well-known that point sources with sufficient mutual distance can be reconstructed exactly from finitely many Fourier measurements by solving a convex optimization problem with Tikhonov-regularization (this property is sometimes…
Recovering a low-complexity signal from its noisy observations by regularization methods is a cornerstone of inverse problems and compressed sensing. Stable recovery ensures that the original signal can be approximated linearly by optimal…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
This paper investigates the sparse optimal allocation of sensors for detecting sparse leaking emission sources. Because of the non-negativity of emission rates, uncertainty associated with parameters in the forward model, and sparsity of…
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…
This paper presents an error analysis of classical and learned Tikhonov regularization schemes for inverse problems. We first demonstrate, both theoretically and numerically, that using a fixed regularization parameter across varying noise…
This note addresses the question of optimally estimating a linear functional of an object acquired through linear observations corrupted by random noise, where optimality pertains to a worst-case setting tied to a symmetric, convex, and…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…