Accurate Low-Dose Iterative CT Reconstruction from Few Projections using Sparse and Non-Local Regularization Functions

TitleAccurate Low-Dose Iterative CT Reconstruction from Few Projections using Sparse and Non-Local Regularization Functions
Publication TypeThesis
Year of Publication2016
AuthorsDebatin, M
Academic DepartmentDissertation, University of Heidelberg
Date Published29.06.2016
Thesis TypeDissertation
KeywordsCompressed Sensing, CT reconstruction, Industrial CT, low-dose, Regularization, under-sampling

This dissertation aims at reducing the dose and the acquisition time in medical and in industrial Computed Tomography (CT). Since X-rays carry enough energy to free electrons from atoms, they are extremely harmful to human cells and therefore the dose in X-ray CT should be as low as possible. For industrial CT, short acquisition and reconstruction times decrease the availability time of the X-ray machine and therefore increase the sales, due to a higher throughput. As a matter of principle, there are three strategies to reduce the dose, defined as the product of the tube current and the pulse length of the CT system: (1) Lowering the X-ray exposure by reducing the X-ray tube current; (2) lowering the pulse length of the industrial CT system which allows for a shorter acquisition process as well and (3) acquiring less projection views per full rotation of the source around the object, which enables both, a faster acquisition and reconstruction. However, all of these strategies have a strong negative impact on the resulting image quality, especially when they are combined. (1) and (2) introduce additional noise and (3) leads to streaking artifacts in the reconstructed images. Therefore, efficient reconstruction algorithms have to be found which can compensate the resulting image quality degradation. The X-ray model can be solved analytically by Filtered Backprojection (FBP) or iteratively by solving (regularized) objective functions. Up to now, commercial scanners still employ analytical FBP due to its fast execution times. However, the aforementioned strategies of dose reduction are not suitable for this method: The images are heavily corrupted by noise and artifacts and are therefore not suitable for medical inspection or industrial CT quality control. Total Variation (TV) is the current state of the art method for the regularization term of iterative algorithms in X-ray CT. It can remove the noise and the streaks in the images at the cost of over-smoothing of small-scaled image features and those of small intensity. Furthermore, the images suffer from a loss of contrast and spatial resolution and "stair-casing" artifacts are introduced in image regions which should be homogeneous. This dissertation presents three new regularization functions for low-dose, under-sampled, iterative CT which successively improve the reconstruction results of the current state of the art techniques: FBP and Total Variation. The first method is called the Anisotropic Total Variation (ATV). We propose a gradient re-definition so as to overcome TV's problem of over-smoothing fine structures. The re-definition is accomplished by multiplying the gradient in the definition of TV by an exponential function. We include a parameter in this function and this parameter acts like a threshold of the noise and controls which structures (noise and prominent edges) to penalize during the reconstruction. The second method focuses on the main drawbacks of TV: The production of stair-casing artifacts in regions which should be homogeneous and the over-smoothing of fine structures. To reduce the stair-casing effect of TV and at the same time to reconstruct high resolution images, we combine first and second order derivatives and we create a new regularization function. The first order Anisotropic Total Variation can separate noise and prominent edges up to a certain noise magnitude and the second order Total Variation better penalizes undesired edges than first order TV. The resulting method is called ATV+TV².The third method discusses a novel generalization of TV. It is called Generalized Anisotropic Total Variation (GATV). GATV uses a priori information about the Gradient Magnitude Distribution (GMD) of the underlying object for the reconstruction. By efficient parameterization, this method can separate noise and prominent image features and it can therefore overcome the problems of TV and reconstruct high quality CT images. We reconstruct real patient data and digitally simulated phantom data. We evaluate the efficiency of our proposed regularization methods based on a large experiment with 560 measurements where different numbers of projections, noise levels and 10 different realizations of the noise random variable were selected. We judge the results from a qualitative point of view by analyzing the reconstructed images in terms of edge sharpness and accuracy, image homogeneity and image details, like small structures and features. Furthermore, we apply quantitative measures to assess the image quality: The Relative Root Mean Squared Error (RRMSE), the Contrast to Noise Ratio (CNR), the Kullback-Leibler distance and a measure to rate the spatial resolution and the homogeneity of the image. The main findings of this dissertation indicate that all of the three methods successively improve the visual impression of the reconstruction results in terms of preservation of small-scaled image features and features of small intensity. Furthermore, they can improve the edge sharpness and accuracy, spatial resolution, image contrast and homogeneity and each method, ATV, ATV+TV² and GATV, thereby improves the reconstruction results of its preceding method. In case of noise-free projections, GATV can accurately reconstruct digitally simulated data from 20 projections and it can achieve a RRMSE which is up to 1770 times smaller than the RRMSE of TV. In case of noisy projections, all of the three methods can achieve an extreme dose reduction factor of approximately 16 compared to the results of TV. Furthermore, at this reduction factor, ATV, ATV+TV² and GATV can still lower the RRMSE by approximately 11%, 20% and 33% compared to the results of TV, obtained from a high dose and many view setting. From previous publications (Xun Jia et al., Medical physics, 37:1757, 2010) we know that a 72 times dose reduction can be achieved for a TV regularized iterative reconstruction compared to FBP. Combining this information with the dose reduction potential of the proposed methods, ATV, ATV+TV² and GATV, reveals the potential to decrease the dose and acquisition time in CT by a factor of approximately three orders of magnitude (1000), compared to conventional FBP.

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