Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

Kavli Affiliate: Eric Miller

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

| Summary:

We introduce PaLEnTIR, a significantly enhanced parametric level-set (PaLS)
method addressing the restoration and reconstruction of piecewise constant
objects. Our key contribution involves a unique PaLS formulation utilizing a
single level-set function to restore scenes containing multi-contrast
piecewise-constant objects without requiring knowledge of the number of objects
or their contrasts. Unlike standard PaLS methods employing radial basis
functions (RBFs), our model integrates anisotropic basis functions (ABFs),
thereby expanding its capacity to represent a wider class of shapes.
Furthermore, PaLEnTIR improves the conditioning of the Jacobian matrix,
required as part of the parameter identification process, and consequently
accelerates optimization methods. We validate PaLEnTIR’s efficacy through
diverse experiments encompassing sparse and limited angle of view X-ray
computed tomography (2D and 3D), nonlinear diffuse optical tomography (DOT),
denoising, and deconvolution tasks using both real and simulated data sets.

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