Fourth-Order Nonlocal Tensor Decomposition Model for Spectral Computed Tomography

TL;DR

This paper introduces a novel fourth-order nonlocal tensor decomposition model for spectral CT image reconstruction, effectively reducing noise and preserving details by leveraging spatial and spectral similarities and advanced optimization techniques.

Contribution

The proposed FONT-SIR method combines nonlocal tensor modeling, PCA-based feature extraction, and low-rank plus sparsity constraints with ADMM optimization for improved spectral CT reconstruction.

Findings

Superior noise suppression compared to existing methods

Enhanced detail preservation in reconstructed images

Validated on both simulated and real datasets

Abstract

Spectral computed tomography (CT) can reconstruct spectral images from different energy bins using photon counting detectors (PCDs). However, due to the limited photons and counting rate in the corresponding spectral fraction, the reconstructed spectral images usually suffer from severe noise. In this paper, a fourth-order nonlocal tensor decomposition model for spectral CT image reconstruction (FONT-SIR) method is proposed. Similar patches are collected in both spatial and spectral dimensions simultaneously to form the basic tensor unit. Additionally, principal component analysis (PCA) is applied to extract latent features from the patches for a robust and efficient similarity measure. Then, low-rank and sparsity decomposition is performed on the produced fourth-order tensor unit, and the weighted nuclear norm and total variation (TV) norm are used to enforce the low-rank and sparsity constraints, respectively. The alternating direction method of multipliers (ADMM) is adopted to optimize the objective function. The experimental results with our proposed FONT-SIR demonstrates a superior qualitative and quantitative performance for both simulated and real data sets relative to several state-of-the-art methods, in terms of noise suppression and detail preservation.