Related papers: Information field theory
The virtues of an effective field theory (EFT) approach to many-body problems are illustrated by deriving the expansion for the energy of an homogeneous, interacting Fermi gas at low density and zero temperature. A renormalization scheme…
Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle…
Transmitted data may be corrupted by both noise and data loss. Grassmannian frames are in some sense optimal representations of data transmitted over a noisy channel that may lose some of the transmitted coefficients. Fusion frame (or frame…
We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…
Density functional theory (DFT) exploits an independent-particle-system construction to replicate the densities and current of an interacting system. This construction is used here to access the exact effective potential and bias of…
The topic of this paper is a novel Bayesian continuous-basis field representation and inference framework. Within this paper several problems are solved: The maximally informative inference of continuous-basis fields, that is where the…
Electrical Impedance Tomography (EIT) is a powerful imaging modality widely used in medical diagnostics, industrial monitoring, and environmental studies. The EIT inverse problem is about inferring the internal conductivity distribution of…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…
In this paper, we address the fusion problem in wireless sensor networks, where the cross-correlation between the estimates is unknown. To solve the problem within the Bayesian framework, we assume that the covariance matrix has a prior…
The nervous system solves a wide variety of problems in signal processing. In many cases the performance of the nervous system is so good that it apporaches fundamental physical limits, such as the limits imposed by diffraction and photon…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Bayesian inference for inverse problems hinges critically on the choice of priors. In the absence of specific prior information, population-level distributions can serve as effective priors for parameters of interest. With the advent of…
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…
Effective Field Theories (EFTs) constructed as derivative expansions in powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a controllable approximation to strong dynamics as long as the energy of the interacting…
We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
Electrical impedance tomography (EIT) is a non-invasive imaging method in which an unknown physical body is probed with electric currents applied on the boundary, and the internal conductivity distribution is recovered from the measured…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…