534,350 research outputs found
Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)
In this paper, we consider the restoration and reconstruction of piecewise
constant objects in two and three dimensions using PaLEnTIR, a significantly
enhanced Parametric level set (PaLS) model relative to the current
state-of-the-art. The primary contribution of this paper is a new PaLS
formulation which requires only a single level set function to recover a scene
with piecewise constant objects possessing multiple unknown contrasts. Our
model offers distinct advantages over current approaches to the multi-contrast,
multi-object problem, all of which require multiple level sets and explicit
estimation of the contrast magnitudes. Given upper and lower bounds on the
contrast, our approach is able to recover objects with any distribution of
contrasts and eliminates the need to know either the number of contrasts in a
given scene or their values. We provide an iterative process for finding these
space-varying contrast limits. Relative to most PaLS methods which employ
radial basis functions (RBFs), our model makes use of non-isotropic basis
functions, thereby expanding the class of shapes that a PaLS model of a given
complexity can approximate. Finally, PaLEnTIR improves the conditioning of the
Jacobian matrix required as part of the parameter identification process and
consequently accelerates the optimization methods by controlling the magnitude
of the PaLS expansion coefficients, fixing the centers of the basis functions,
and the uniqueness of parametric to image mappings provided by the new
parameterization. We demonstrate the performance of the new approach using both
2D and 3D variants of X-ray computed tomography, diffuse optical tomography
(DOT), denoising, deconvolution problems. Application to experimental sparse CT
data and simulated data with different types of noise are performed to further
validate the proposed method.Comment: 31 pages, 56 figure
A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems
We introduce a derivative-free computational framework for approximating
solutions to nonlinear PDE-constrained inverse problems. The aim is to merge
ideas from iterative regularization with ensemble Kalman methods from Bayesian
inference to develop a derivative-free stable method easy to implement in
applications where the PDE (forward) model is only accessible as a black box.
The method can be derived as an approximation of the regularizing
Levenberg-Marquardt (LM) scheme [14] in which the derivative of the forward
operator and its adjoint are replaced with empirical covariances from an
ensemble of elements from the admissible space of solutions. The resulting
ensemble method consists of an update formula that is applied to each ensemble
member and that has a regularization parameter selected in a similar fashion to
the one in the LM scheme. Moreover, an early termination of the scheme is
proposed according to a discrepancy principle-type of criterion. The proposed
method can be also viewed as a regularizing version of standard Kalman
approaches which are often unstable unless ad-hoc fixes, such as covariance
localization, are implemented. We provide a numerical investigation of the
conditions under which the proposed method inherits the regularizing properties
of the LM scheme of [14]. More concretely, we study the effect of ensemble
size, number of measurements, selection of initial ensemble and tunable
parameters on the performance of the method. The numerical investigation is
carried out with synthetic experiments on two model inverse problems: (i)
identification of conductivity on a Darcy flow model and (ii) electrical
impedance tomography with the complete electrode model. We further demonstrate
the potential application of the method in solving shape identification
problems by means of a level-set approach for the parameterization of unknown
geometries
Parameter identification problems in the modelling of cell motility
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference between the computed and observed data are proposed and the parameter identification problem is formulated as a minimisation problem of nonlinear least squares type. A Levenberg–Marquardt based optimisation method is applied to the solution of the minimisation problem and the details of the implementation are discussed. A number of numerical experiments are presented which illustrate the robustness of the algorithm to parameter identification in the presence of large deformations and noisy data and parameter identification in three dimensional models of cell motility. An application to experimental data is also presented in which we seek to identify parameters in a model for the monopolar growth of fission yeast cells using experimental imaging data. Our numerical tests allow us to compare the method with the two different formulations of the objective functional and we conclude that the results with both objective functionals seem to agree
On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification
We present a new approach to convexification of the Tikhonov regularization
using a continuation method strategy. We embed the original minimization
problem into a one-parameter family of minimization problems. Both the penalty
term and the minimizer of the Tikhonov functional become dependent on a
continuation parameter.
In this way we can independently treat two main roles of the regularization
term, which are stabilization of the ill-posed problem and introduction of the
a priori knowledge. For zero continuation parameter we solve a relaxed
regularization problem, which stabilizes the ill-posed problem in a weaker
sense. The problem is recast to the original minimization by the continuation
method and so the a priori knowledge is enforced.
We apply this approach in the context of topology-to-shape geometry
identification, where it allows to avoid the convergence of gradient-based
methods to a local minima. We present illustrative results for magnetic
induction tomography which is an example of PDE constrained inverse problem
A nested mixture model for protein identification using mass spectrometry
Mass spectrometry provides a high-throughput way to identify proteins in
biological samples. In a typical experiment, proteins in a sample are first
broken into their constituent peptides. The resulting mixture of peptides is
then subjected to mass spectrometry, which generates thousands of spectra, each
characteristic of its generating peptide. Here we consider the problem of
inferring, from these spectra, which proteins and peptides are present in the
sample. We develop a statistical approach to the problem, based on a nested
mixture model. In contrast to commonly used two-stage approaches, this model
provides a one-stage solution that simultaneously identifies which proteins are
present, and which peptides are correctly identified. In this way our model
incorporates the evidence feedback between proteins and their constituent
peptides. Using simulated data and a yeast data set, we compare and contrast
our method with existing widely used approaches (PeptideProphet/ProteinProphet)
and with a recently published new approach, HSM. For peptide identification,
our single-stage approach yields consistently more accurate results. For
protein identification the methods have similar accuracy in most settings,
although we exhibit some scenarios in which the existing methods perform
poorly.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS316 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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