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.

翻译：我们提出PaLEnTIR方法，一种显著增强的参数化水平集（PaLS）技术，用于解决分段常数物体的恢复与重建问题。核心贡献在于提出独特的PaLS公式，通过单一水平集函数重建包含多对比度分段常数场景，而无需预知物体数量或对比度值。与传统采用径向基函数（RBFs）的标准PaLS方法不同，本模型整合各向异性基函数（ABFs），从而扩展对更广泛形状的表示能力。此外，PaLEnTIR改善了参数识别过程中雅可比矩阵的条件数，进而加速优化方法收敛。通过涵盖稀疏与有限角度CT成像（2D与3D）、非线性扩散光学层析成像（DOT）、去噪及去卷积等多种实验（基于真实与模拟数据集），我们验证了PaLEnTIR的有效性。