11,198 research outputs found
Expectation Propagation for Poisson Data
The Poisson distribution arises naturally when dealing with data involving
counts, and it has found many applications in inverse problems and imaging. In
this work, we develop an approximate Bayesian inference technique based on
expectation propagation for approximating the posterior distribution formed
from the Poisson likelihood function and a Laplace type prior distribution,
e.g., the anisotropic total variation prior. The approach iteratively yields a
Gaussian approximation, and at each iteration, it updates the Gaussian
approximation to one factor of the posterior distribution by moment matching.
We derive explicit update formulas in terms of one-dimensional integrals, and
also discuss stable and efficient quadrature rules for evaluating these
integrals. The method is showcased on two-dimensional PET images.Comment: 25 pages, to be published at Inverse Problem
Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes
Effective modeling and numerical spectral-based propagation schemes are
proposed for addressing the challenges in time-dependent quantum simulations of
systems ranging from atoms, molecules, and nanostructures to emerging
nanoelectronic devices. While time-dependent Hamiltonian problems can be
formally solved by propagating the solutions along tiny simulation time steps,
a direct numerical treatment is often considered too computationally demanding.
In this paper, however, we propose to go beyond these limitations by
introducing high-performance numerical propagation schemes to compute the
solution of the time-ordered evolution operator. In addition to the direct
Hamiltonian diagonalizations that can be efficiently performed using the new
eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a
basis transformed propagation scheme (BTPS) which allow to reduce considerably
the simulation times needed by time intervals. It is outlined that BTPS offers
the best computational efficiency allowing new perspectives in time-dependent
simulations. Finally, these numerical schemes are applied to study the AC
response of a (5,5) carbon nanotube within a 3D real-space mesh framework
On Approximate Nonlinear Gaussian Message Passing On Factor Graphs
Factor graphs have recently gained increasing attention as a unified
framework for representing and constructing algorithms for signal processing,
estimation, and control. One capability that does not seem to be well explored
within the factor graph tool kit is the ability to handle deterministic
nonlinear transformations, such as those occurring in nonlinear filtering and
smoothing problems, using tabulated message passing rules. In this
contribution, we provide general forward (filtering) and backward (smoothing)
approximate Gaussian message passing rules for deterministic nonlinear
transformation nodes in arbitrary factor graphs fulfilling a Markov property,
based on numerical quadrature procedures for the forward pass and a
Rauch-Tung-Striebel-type approximation of the backward pass. These message
passing rules can be employed for deriving many algorithms for solving
nonlinear problems using factor graphs, as is illustrated by the proposition of
a nonlinear modified Bryson-Frazier (MBF) smoother based on the presented
message passing rules
- …