Parametric Level-sets Enhanced To Improve Reconstruction (PaLEnTIR)
This is an incremental improvement for imaging and tomography applications, enhancing reconstruction of multi-contrast objects without prior knowledge.
The paper tackles the problem of restoring and reconstructing piecewise constant objects by introducing PaLEnTIR, an enhanced parametric level-set method that uses anisotropic basis functions and improves Jacobian conditioning, achieving faster optimization and validated across tasks like X-ray CT and optical tomography.
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.