472 research outputs found
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
We consider continuous-time sparse stochastic processes from which we have
only a finite number of noisy/noiseless samples. Our goal is to estimate the
noiseless samples (denoising) and the signal in-between (interpolation
problem).
By relying on tools from the theory of splines, we derive the joint a priori
distribution of the samples and show how this probability density function can
be factorized. The factorization enables us to tractably implement the maximum
a posteriori and minimum mean-square error (MMSE) criteria as two statistical
approaches for estimating the unknowns. We compare the derived statistical
methods with well-known techniques for the recovery of sparse signals, such as
the norm and Log (- relaxation) regularization
methods. The simulation results show that, under certain conditions, the
performance of the regularization techniques can be very close to that of the
MMSE estimator.Comment: To appear in IEEE TS
Isotropic inverse-problem approach for two-dimensional phase unwrapping
In this paper, we propose a new technique for two-dimensional phase
unwrapping. The unwrapped phase is found as the solution of an inverse problem
that consists in the minimization of an energy functional. The latter includes
a weighted data-fidelity term that favors sparsity in the error between the
true and wrapped phase differences, as well as a regularizer based on
higher-order total-variation. One desirable feature of our method is its
rotation invariance, which allows it to unwrap a much larger class of images
compared to the state of the art. We demonstrate the effectiveness of our
method through several experiments on simulated and real data obtained through
the tomographic phase microscope. The proposed method can enhance the
applicability and outreach of techniques that rely on quantitative phase
evaluation
Structure tensor total variation
This is the final version of the article. Available from Society for Industrial and Applied Mathematics via the DOI in this record.We introduce a novel generic energy functional that we employ to solve inverse imaging problems
within a variational framework. The proposed regularization family, termed as structure tensor
total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both
grayscale and vector-valued images. It generalizes several existing variational penalties, including
the total variation seminorm and vectorial extensions of it. Meanwhile, thanks to the structure
tensor’s ability to capture first-order information around a local neighborhood, the STV functionals
can provide more robust measures of image variation. Further, we prove that the STV regularizers
are convex while they also satisfy several invariance properties w.r.t. image transformations. These
properties qualify them as ideal candidates for imaging applications. In addition, for the discrete
version of the STV functionals we derive an equivalent definition that is based on the patch-based
Jacobian operator, a novel linear operator which extends the Jacobian matrix. This alternative
definition allow us to derive a dual problem formulation. The duality of the problem paves the
way for employing robust tools from convex optimization and enables us to design an efficient
and parallelizable optimization algorithm. Finally, we present extensive experiments on various
inverse imaging problems, where we compare our regularizers with other competing regularization
approaches. Our results are shown to be systematically superior, both quantitatively and visually
A Learning Approach to Optical Tomography
We describe a method for imaging 3D objects in a tomographic configuration
implemented by training an artificial neural network to reproduce the complex
amplitude of the experimentally measured scattered light. The network is
designed such that the voxel values of the refractive index of the 3D object
are the variables that are adapted during the training process. We demonstrate
the method experimentally by forming images of the 3D refractive index
distribution of cells
A dynamical description of neutron star crusts
Neutron Stars are natural laboratories where fundamental properties of matter
under extreme conditions can be explored. Modern nuclear physics input as well
as many-body theories are valuable tools which may allow us to improve our
understanding of the physics of those compact objects.
In this work the occurrence of exotic structures in the outermost layers of
neutron stars is investigated within the framework of a microscopic model. In
this approach the nucleonic dynamics is described by a time-dependent mean
field approach at around zero temperature. Starting from an initial crystalline
lattice of nuclei at subnuclear densities the system evolves toward a manifold
of self-organized structures with different shapes and similar energies. These
structures are studied in terms of a phase diagram in density and the
corresponding sensitivity to the isospin-dependent part of the equation of
state and to the isotopic composition is investigated.Comment: 8 pages, 5 figures, conference NN201
Matérn B-Splines and the Optimal Reconstruction of Signals
Starting from the power spectral density of Matérn stochastic processes, we introduce a new family of splines that is defined in terms of the whitening operator of such processes. We show that these Matérn splines admit a stable representation in a B-spline-like basis. We specify the Matérn B-splines (causal and symmetric) and identify their key properties; in particular, we prove that these generate a Riesz basis and that they can be written as a product of an exponential with a fractional polynomial B-spline. We also indicate how these new functions bridge the gap between the fractional polynomial splines and the cardinal exponential ones. We then show that these splines provide the optimal reconstruction space for the minimum mean-squared error estimation of Matérn signals from their noisy samples. We also propose a digital Wiener-filter-like algorithm for the efficient determination of the optimal B-spline coefficients
An Optimized Spline-Based Registration of a 3D CT to a Set of C-Arm Images
We have developed an algorithm for the rigid-body registration of
a CT volume to a set of C-arm images.
The algorithm uses a gradient-based iterative minimization of a least-squares measure
of dissimilarity between the C-arm images and projections of the
CT volume. To compute projections, we use a novel method for fast
integration of the volume along rays. To improve robustness and
speed, we take advantage of a coarse-to-fine processing of the
volume/image pyramids. To compute the projections of the volume,
the gradient of the dissimilarity measure, and the multiresolution
data pyramids, we use a continuous image/volume model based on
cubic B-splines, which ensures a high interpolation accuracy and a
gradient of the dissimilarity measure that is well defined
everywhere. We show the performance of our algorithm on a human
spine phantom, where the true alignment is determined using a set
of fiducial markers
Logarithmic transformation technique for exact signal recovery in frequency-domain optical-coherence tomography
AN APPEAL FROM A JUDGMENT AND DECREE OF DIVORCE OF THE THIRD JUDICIAL DISTRICT, SALT LAKE COUNTY, UTAH THE HONORABLE JOHN A. ROKICH JUDGE PRESIDING
Approximate Message Passing with Consistent Parameter Estimation and Applications to Sparse Learning
We consider the estimation of an i.i.d. (possibly non-Gaussian) vector \xbf
\in \R^n from measurements \ybf \in \R^m obtained by a general cascade model
consisting of a known linear transform followed by a probabilistic
componentwise (possibly nonlinear) measurement channel. A novel method, called
adaptive generalized approximate message passing (Adaptive GAMP), that enables
joint learning of the statistics of the prior and measurement channel along
with estimation of the unknown vector \xbf is presented. The proposed
algorithm is a generalization of a recently-developed EM-GAMP that uses
expectation-maximization (EM) iterations where the posteriors in the E-steps
are computed via approximate message passing. The methodology can be applied to
a large class of learning problems including the learning of sparse priors in
compressed sensing or identification of linear-nonlinear cascade models in
dynamical systems and neural spiking processes. We prove that for large i.i.d.
Gaussian transform matrices the asymptotic componentwise behavior of the
adaptive GAMP algorithm is predicted by a simple set of scalar state evolution
equations. In addition, we show that when a certain maximum-likelihood
estimation can be performed in each step, the adaptive GAMP method can yield
asymptotically consistent parameter estimates, which implies that the algorithm
achieves a reconstruction quality equivalent to the oracle algorithm that knows
the correct parameter values. Remarkably, this result applies to essentially
arbitrary parametrizations of the unknown distributions, including ones that
are nonlinear and non-Gaussian. The adaptive GAMP methodology thus provides a
systematic, general and computationally efficient method applicable to a large
range of complex linear-nonlinear models with provable guarantees.Comment: 14 pages, 3 figure
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