Non-Local Low-Rank Cube-Based Tensor Factorization for Spectral CT Reconstruction

Abstract

Spectralcomputed tomography (CT) reconstructs material-dependent attenuation images from the projections of multiple narrow energy windows which is meaningful for material identification and decomposition. Unfortunately, the multi-energy projection datasets usually have lower signal-noise-ratios (SNR). Very recently, a spatial-spectral cube matching frame (SSCMF) was proposed to explore the non-local spatial-spectral similarities for spectral CT. This method constructs a group by clustering up a series of non-local spatial-spectral cubes. The small size of spatial patches for such a group makes the SSCMF fail to fully encode the sparsity and low-rank properties. The hard-thresholding and collaboration filtering in the SSCMF also cause difficulty in recovering the image features and spatial edges. While all the steps are operated on 4-D group, the huge computational cost and memory load might not be affordable in practice. To avoid the above limitations and further improve image quality, we first formulate a non-local cube-based tensor instead of group to encode the sparsity and low-rank properties. Then, as a new regularizer, the Kronecker-Basis-Representation (KBR) tensor factorization is employed into a basic spectral CT reconstruction model to enhance the capability of image feature extraction and spatial edge preservation, generating a non-local low-rank cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman method is adopted to solve the NLCTF model. Both numerical simulations and preclinical mouse studies are performed to validate and evaluate the NLCTF algorithm. The results show that the NLCTF method outperforms other state-ofthe-art competing algorithms.

Artificial intelligence in image reconstruction: The change is here

“…Considering sparsity and low-rank properties in the spatialspectral domain, multiple dedicated algorithms were developed using tensor-based nuclear norm [148], prior rank, intensity and sparsity model [149,150], total nuclear variation [151], patch-based low-rank [152], structure tensor TV [153], and tensor dictionary learning [154,155]. To further improve the reconstructed image quality, the nonlocal image similarity was explored in spectral CT reconstruction, including nonlocal low-rank and sparse matrix decomposition [156], spatial-spectral non-local means [157], nonlocal spectral similarity [158], spatial-spectral cube matching frame (SSCMF) [159], non-local low-rank cube-based tensor factorization (NLCTF) [160], and so on. All these methods were designed for two-dimensional cases.…”

Multiple Characteristics Similarity Metric Method for Hyperspectral Image Classification

“…For HSI classification, SRC means that a test sample can be linearly represented by the training samples via l 0 -norm or l 1 -norm [37], [38], which reveals the sparse property of HSI data. While CRC emphasizes that all the training samples are equal to represent a test sample by l 2 -norm regularized term, which provides collaborative characteristic of HSI data.…”

Image-Domain Based Material Decomposition by Multi-Constraint Optimization for Spectral CT

“…The image-domain based methods [19,20] firstly reconstruct images from the spectral CT dataset and then decompose the materials from the reconstructed results. There are many iterative reconstruction methods developed for the first step, but less work concerned about the second step, such as TDL [21], L0TDL [22], SSCMF [23], NLCTF [24], ASSIST [25], L0-PICCS [26], SISTER [27]. In this work, we focus on the second step of the image-domain based methods.…”