Kavli Affiliate: Eric Miller
| First 5 Authors: Ege Ozsar, Misha Kilmer, Eric Miller, Eric de Sturler, Arvind Saibaba
| Summary:
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.
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