CT IMAGE RECONSTRUCTION ON A LOW DIMENSIONAL MANIFOLD

Tomographic Image Reconstruction Using an Advanced Score Function (ADSF)

Computed tomography (CT) reconstructs volumetric images using X-ray projection data acquired from multiple angles around an object. For low-dose or sparse-view CT scans, the classic image reconstruction algorithms often produce severe noise and artifacts. To address this issue, we develop a novel iterative image reconstruction method based on maximum a posteriori (MAP) estimation. In the MAP framework, the score function, i.e., the gradient of the logarithmic probability density distribution, plays a crucial role as an image prior in the iterative image reconstruction process. By leveraging the Gaussian mixture model, we derive a novel score matching formula to establish an advanced score function (ADSF) through deep learning. Integrating the new ADSF into the image reconstruction process, a new ADSF iterative reconstruction method is developed to improve image reconstruction quality. The convergence of the ADSF iterative reconstruction algorithm is proven through mathematical analysis. The performance of the ADSF reconstruction method is also evaluated on both public medical image datasets and clinical raw CT datasets. Our results show that the ADSF reconstruction method can achieve better denoising and deblurring effects than the state-of-the-art reconstruction methods, showing excellent generalizability and stability.

Low-dimensional Manifold Constrained Disentanglement Network for Metal Artifact Reduction

Deep neural network based methods have achieved promising results for CT metal artifact reduction (MAR), most of which use many synthesized paired images for supervised learning. As synthesized metal artifacts in CT images may not accurately reflect the clinical counterparts, an artifact disentanglement network (ADN) was proposed with unpaired clinical images directly, producing promising results on clinical datasets. However, as the discriminator can only judge if large regions semantically look artifact-free or artifact-affected, it is difficult for ADN to recover small structural details of artifact-affected CT images based on adversarial losses only without sufficient constraints. To overcome the illposedness of this problem, here we propose a low-dimensional manifold (LDM) constrained disentanglement network (DN), leveraging the image characteristics that the patch manifold of CT images is generally low-dimensional. Specifically, we design an LDM-DN learning algorithm to empower the disentanglement network through optimizing the synergistic loss functions used in ADN while constraining the recovered images to be on a low-dimensional patch manifold. Moreover, learning from both paired and unpaired data, an efficient hybrid optimization scheme is proposed to further improve the MAR performance on clinical datasets. Extensive experiments demonstrate that the proposed LDM-DN approach can consistently improve the MAR performance in paired and/or unpaired learning settings, outperforming competing methods on synthesized and clinical datasets.

Stabilizing deep tomographic reconstruction: Part A. Hybrid framework and experimental results

A recent PNAS paper reveals that several popular deep reconstruction networks are unstable. Specifically, three kinds of instabilities were reported: (1) strong image artefacts from tiny perturbations, (2) small features missed in a deeply reconstructed image, and (3) decreased imaging performance with increased input data. Here, we propose an analytic compressed iterative deep (ACID) framework to address this challenge. ACID synergizes a deep network trained on big data, kernel awareness from compressed sensing (CS)-inspired processing, and iterative refinement to minimize the data residual relative to real measurement. Our study demonstrates that the ACID reconstruction is accurate, is stable, and sheds light on the converging mechanism of the ACID iteration under a bounded relative error norm assumption. ACID not only stabilizes an unstable deep reconstruction network but also is resilient against adversarial attacks to the whole ACID workflow, being superior to classic sparsity-regularized reconstruction and eliminating the three kinds of instabilities.

Exterior computed tomography image reconstruction based on anisotropic relative total variation in polar coordinates

In computed tomography (CT) image reconstruction problems, exterior CT is an important application in industrial non-destructive testing (NDT). Different from the limited-angle problem that misses part of the rotation angle, the rotation angle of the exterior problem is complete, but for each rotation angle, the projection data through the central region of the object cannot be collected, so that the exterior CT problem is ill-posed inverse problem. The results of traditional reconstruction methods like filtered back-projection (FBP) and simultaneous algebra reconstruction technique (SART) have artifacts along the radial direction edges for exterior CT reconstruction. In this study, we propose and test an anisotropic relative total variation in polar coordinates (P-ARTV) model for addressing the exterior CT problem. Since relative total variation (RTV) can effectively distinguish edges from noises, and P-ARTV with different weights in radial and tangential directions can effectively enhance radial edges, a two-step iteration algorithm was developed to solve the P-ARTV model in this study. The fidelity term and the regularization term are solved in Cartesian and polar coordinate systems, respectively. Numerical experiments show that our new model yields better performance than the existing state-of-the-art algorithms.

Classification of Infrared Objects in Manifold Space Using Kullback-Leibler Divergence of Gaussian Distributions of Image Points

Infrared image recognition technology can work day and night and has a long detection distance. However, the infrared objects have less prior information and external factors in the real-world environment easily interfere with them. Therefore, infrared object classification is a very challenging research area. Manifold learning can be used to improve the classification accuracy of infrared images in the manifold space. In this article, we propose a novel manifold learning algorithm for infrared object detection and classification. First, a manifold space is constructed with each pixel of the infrared object image as a dimension. Infrared images are represented as data points in this constructed manifold space. Next, we simulate the probability distribution information of infrared data points with the Gaussian distribution in the manifold space. Then, based on the Gaussian distribution information in the manifold space, the distribution characteristics of the data points of the infrared image in the low-dimensional space are derived. The proposed algorithm uses the Kullback-Leibler (KL) divergence to minimize the loss function between two symmetrical distributions, and finally completes the classification in the low-dimensional manifold space. The efficiency of the algorithm is validated on two public infrared image data sets. The experiments show that the proposed method has a 97.46% classification accuracy and competitive speed in regards to the analyzed data sets.