Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)

TL;DR

PaLEnTIR introduces an advanced parametric level-set method that effectively reconstructs piecewise constant objects with multi-contrast features, improving shape representation and computational efficiency across various imaging modalities.

Contribution

It presents a novel PaLS formulation with anisotropic basis functions and enhanced Jacobian conditioning, enabling accurate reconstruction without prior object number or contrast knowledge.

Findings

Effective in sparse and limited-angle X-ray CT reconstructions

Improves shape representation with anisotropic basis functions

Accelerates optimization through better Jacobian conditioning

Abstract

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.