Jiang Hsieh

Low-Dose X-ray CT Reconstruction via Dictionary Learning

Although diagnostic medical imaging provides enormous benefits in the early detection and accuracy diagnosis of various diseases, there are growing concerns on the potential side effect of radiation induced genetic, cancerous and other diseases. How to reduce radiation dose while maintaining the diagnostic performance is a major challenge in the computed tomography (CT) field. Inspired by the compressive sensing theory, the sparse constraint in terms of total variation (TV) minimization has already led to promising results for low-dose CT reconstruction. Compared to the discrete gradient transform used in the TV method, dictionary learning is proven to be an effective way for sparse representation. On the other hand, it is important to consider the statistical property of projection data in the low-dose CT case. Recently, we have developed a dictionary learning based approach for low-dose X-ray CT. In this paper, we present this method in detail and evaluate it in experiments. In our method, the sparse constraint in terms of a redundant dictionary is incorporated into an objective function in a statistical iterative reconstruction framework. The dictionary can be either predetermined before an image reconstruction task or adaptively defined during the reconstruction process. An alternating minimization scheme is developed to minimize the objective function. Our approach is evaluated with low-dose X-ray projections collected in animal and human CT studies, and the improvement associated with dictionary learning is quantified relative to filtered backprojection and TV-based reconstructions. The results show that the proposed approach might produce better images with lower noise and more detailed structural features in our selected cases. However, there is no proof that this is true for all kinds of structures.

Data consistency based translational motion artifact reduction in fan-beam CT

A basic assumption in the classic computed tomography (CT) theory is that an object remains stationary in an entire scan. In biomedical CT/micro-CT, this assumption is often violated. To produce high-resolution images, such as for our recently proposed clinical micro-CT (CMCT) prototype, it is desirable to develop a precise motion estimation and image reconstruction scheme. In this paper, we first extend the Helgason-Ludwig consistency condition (HLCC) from parallel-beam to fan-beam geometry when an object is subject to a translation. Then, we propose a novel method to estimate the motion parameters only from sinograms based on the HLCC. To reconstruct the moving object, we formulate two generalized fan-beam reconstruction methods, which are in filtered backprojection and backprojection filtering formats, respectively. Furthermore, we present numerical simulation results to show that our approach is accurate and robust

Compressive Sensing–based Interior Tomography: Preliminary Clinical Application

Abstract Compressive sensing (CS)-based interior tomography is a state-of-the-art method for accurate image reconstruction from only locally truncated projections. Here, we report our preliminary interior tomography results reconstructed from raw projections of a patient acquired on a GE Discovery CT750 HD scanner. This is the first clinical application of the CS-based interior reconstruction techniques, and the results show an excellent match with those reconstructed from global projections.

Relation between the filtered backprojection algorithm and the backprojection algorithm in CT

In this letter, we present a new fan-beam CT formula, based on which we discuss the relation between the filtered backprojection (FBP) algorithm and the backprojection (BP) algorithm. Specifically, the FBP algorithm can be expressed in a series with its first-order approximation being the BP algorithm. As a result, we identify a link between X-ray CT and number theory.

General formulation for x-ray computed tomography

Over recent years, various exact cone-beam reconstruction algorithms have been proposed. The derivations of these algorithms are quite complicated, and often difficult to see the fundamental connections among these methods and their key steps. In this paper, we present a straightforward perspective based on the Fourier transform, which is a universal principle for parallel and divergent beam computed tomography (CT). The formulas in this paper are not only consistent with the latest findings in the field but also valid under more general conditions.

CT reconstruction filter design in the real space

Theoretically, the ramp filter for filter backprojection reconstruction in X-ray computed tomography (CT) is a generalized function, expressed as |ω| in the frequency domain and -1/(2π2t2) in the real space. The traditional method for designing a practical filter is to select a curve in the frequency domain which is close to the function |Οω| in some sense. Similarly, to design a practical filter one also can select a function in the real space which approximates the function -1/(2π2t2). Several approximations are studied, leading to either known or new filters. The image reconstructed using the new filter is comparable with that using the band-limited filter.