International Journal of Image and Graphics

We investigate the inversion of the 2D Radon transform with the technique based on the Circular Harmonic Transform (CHT) using Chebyshev/Zernike polynomials. This polynomial pair is often described as a solution of the unstable or causal form of the CHT inverse. The primary object of this work is to show analytically and explicitly that the polynomial pair is formally a solution to the stable form of the CHT inverse. Hence it is the first solution of its type to be simultaneously a solution to both forms of the inverse. The stable/unstable dichotomy is not fundamental to the CHT inverse. We validate this claim with numerical experiments and image data. We describe a potential application of the algorithm to MRI imaging with nonlinear gradients.

We investigate the development of a new analytic approach for 3D PET reconstruction by extension of the chord-based approach for X-ray cone-beam tomography (XCBT). The extension is made possible by recognizing a connection that allows one to reformat 3D PET data into effective cone-beam data so that the chord-based approach can be applied. An important advantage of the new approach is that it can work with general PET system geometries, not limited to the conventional circular geometry. In this paper, we consider a rectangular PET system consisting of four flat-panel detectors. We derive exact analytic reconstruction algorithms for this system and evaluate their performances in numerical studies. Our preliminary results indicate that the derived algorithms can yield accurate reconstructions when applied to noiseless PET data that are generated by assuming the ideal projection model. The algorithms are also observed to respond reasonably well to data noise. Currently, our algorithms do not utilize the entire 3D PET data. Potential modifications to the algorithms for enabling the inclusion of the entire 3D PET data for reconstruction, as well as the theoretical significances and potential practical advantages of this new analytic reconstruction approach, are discussed.

This paper deals with the problem of image reconstruction from incomplete projections. A novel fuzzy vector objective optimization model is developed by integrating the fuzzy set theory and vector objective optimization (multi-objective decision-making). The objective function is expressed as a membership function, and the minimum operator is taken as a fuzzy operator. Furthermore, a novel iterative method is proposed to resolve the fuzzy optimization problem. The images reconstructed from simulated noise projections and real projections obtained from an industrial scanner show that the new algorithm can provide higher resolution and better smoothness than the images reconstructed by the transformation method and the conventional iterative method, so it is more feasible for image reconstruction from incomplete projections.

This work presents an inversion algorithm for the exponential Radon transform (ERT) over 180° range of view angles. The algorithm can be applied to two-dimensional parallel beam geometry in single photon emission computed tomography. First the differentiation of the ERT over π is backprojected. A convolutional relation between this backprojected differentiation and the original image is then established. In order to invert the convolution relation, the least-squares method is utilized to obtain a numerically generated filtering kernel, which readily restores the original image. The advantages of the proposed algorithm are, first, it only requires half the view angles of the conventional inversion algorithm, second, it deals with truncation in ERT data in certain situations, and third, the numerically generated filtering kernel can be pre-calculated and stored for later applications. The algorithm is an analytical approach except for the pre-calculated inverse kernel.

Conventionally, the inverse problem of gated cardiac SPECT is solved by reconstructing the images frame-by-frame, ignoring the inter-frame correlation along the time dimension. To compensate for the non-uniform attenuation for quantitative cardiac imaging, iterative image reconstruction has been a choice which could utilize a priori constraint on the inter-frame correlation for a penalized maximum likelihood (ML) solution. However, iterative image reconstruction in the 4D space involves intensive computations. In this paper, an efficient method for 4D gated SPECT reconstruction is developed based on Karhune-Loève (KL) transform and Novikov's inverse formula. The temporal KL transform is first applied on the data sequence to de-correlate the inter-frame correlation and then the 3D principal components in the KL domain are reconstructed frame-by-frame using Novikov's inverse formula with non-uniform attenuation compensation. Finally an inverse KL transform is performed to obtain quantitatively-reconstructed 4D images in the original space. With the proposed method, 4D reconstruction can be achieved at a reasonable computational cost. The results from computer simulations are very encouraging as compared to conventional frame-by-frame filtered back-projection and iterative ordered-subsets ML reconstructions. By discarding high-order KL components for further noise reduction, the computation time could be further reduced.

An interpixel-shifted spectral imaging technique is applied to MEMS-based spectral-domain endoscopic optical coherence tomography (SDEOCT) to enhance signal-to-noise ratio and effective imaging depth for in vivo imaging diagnosis of biological tissue. To validate the enhancements of pixel-shifted SDEOCT, experimental comparisons are presented to image animal and human bladder architectures in vivo and to diagnose human transitional cell cancers. Preliminary study shows that interpixel shifted SDEOCT not only increases the depth of field of SDOCT but also eliminates excessive artifacts induced by spectral aliasing effect, thus improving image contrast in areas with large depths (e.g. over 1.5 mm). These results suggest that endoscopic OCT equipped with interpixel-shifted spectral camera has the potential to enhance the diagnosis of biological tissue in in vivo settings that require a larger field of view in the axial direction, such as papillary bladder tumors with deep surface irregularities (e.g. asperities or invaginations).

Following the rapid advance in applications of Magnetic Resonance (MR) imaging, there is an upsurge in contemporary image analysis. Image analysis techniques are implemented in different ways in the various frameworks of image processing. This paper proposes a new statistical approach. It first analyzes statistical properties of MR data (bulk magnetizations, MR signals, and k-space samples); then based on these statistics and through MR image reconstruction, derives statistical properties of MR image (a single pixel, any two pixels, and a group of pixels — i.e. an image region); finally by using these image statistics establishes a new stochastic image model (the correlated Finite Normal Mixture (cFNM)) and develops a new statistical image analysis method (the extended Expectation-Maximization (eEM) algorithm). The results obtained by using this cFNM-eEM framework demonstrate promise. The novel feature of this approach is that it eliminates heuristic assumptions and ad-hoc conditions in currently employed image analysis techniques and therefore leads to more accurate image analysis results. Although this approach is developed for the conventional MRI, but, following the same strategy and with some modifications, it can be extended to more advanced MRI protocols and other medical imaging modalities.

Digital model of human metabolic system incorporated with real anatomical structure can be seen as an important tool in order to understand and study the processes of metabolism. This paper presented a whole body digital model framework of [¹⁸F]2-fluoro-2-deoxy-D-glucose (FDG) metabolism based on the segmented Visible Human Project (VHP) data set as the anatomical structure framework. First, the blood time-activity curve (BTAC) and the tissues time-activity curves (TTAC) were obtained from kinetic analysis. According to the obtained BTAC and TTACs, a set of corresponding values were assigned to the segmented VHP image frames. Thus a set of dynamic volume data were derived to show the ¹⁸F distribution in human body for the predetermined sampling schedule. Finally, the simulated FDG distribution was visualized by coronal, axial, and sagittal slices and volume rendering method. The model established here was especially for the metabolism of FDG; however, the modeling method is general for all tracers. The proposed model represented functional information of dynamical process of human metabolism with high visualization resolution. The results of modeling and visualization provide a useful tool for education and research on nuclear imaging, and may provide a novel technical platform for the study of pharmacokinetics.

With the rapid development of multi-detector computed tomography (MDCT) that results in improving the temporal and spatial resolution of patient data, clinical use of computed tomographic angiography (CTA) is increasing. Vessel segmentation can be challenging in CTA, but is needed for isolation of vascular structures. In this paper, a novel method for computation of vesselness in CTA images is presented, including a CTA transfer function prior to the vesselness computation for reducing the artifacts caused by the false-positive responses of a Hessian-based line filter, as well as a hierarchical structure, called MIP-volume pyramid, for accelerating the computation of vesselness. Using the computed vesselness, we present an interactive segmentation method for each individual vessel by applying a vesselness speed function in a fast marching level set method. Our new method was shown to provide an effective and efficient way that allows vesselness to be applied to large CTA images. This method has been implemented successfully in CTA vessel segmentation and evaluation.

In a research context in which multiple and well-behaved Surface Reconstruction algorithms already exist, the main goal is not to implement a visualization toolkit able render complex object, but the implementation of methods which can improve our knowledge on the observed world. This work presents a general Surface Reconstruction framework which encapsulates the uncertainty of the sampled data, making no assumption on the shape of the surface to be reconstructed. Starting from the input points (either points clouds or multiple range images), an Estimated Existence Function (EEF) is built which models the space in which the desired surface could exist and, by the extraction of EEF critical points, the surface is reconstructed. The final goal is the development of a generic framework that is able to adapt the result to different kinds of additional information coming that is from multiple sensors.

The paper developed an approach to extract the VOI (Volume of Interest) from a CT dataset based on volume rendering, which can get a rough VOI from the volumetric data by simply adjusting the Window Level and the Window Width, then enhances the contrast among the voxels according to the Linear General Fuzzy Operator (LGFO) and extracts a desired structure from the above-mentioned enhanced 3D data through the feature function in rapid sequence; Our method adjusts the parameters according to the condition until the satisfied VOI is extracted. Experimental results show that the method combined with multi-manner can extract the VOI which represents clearly three dimensional anatomical structure of the object, such as tumors or normal organs, and can find potential applications in diagnosis and education.