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The recent application of Fourier Based Iterative Reconstruction Method (FIRM) has made it possible to achieve high-quality 2D images from a fan beam Computed Tomography (CT) scan with a limited number of projections in a fast manner. The proposed methodology in this article is designed to provide 3D Radon space in linogram fashion to facilitate the use of FIRM with cone beam projections (CBP) for the reconstruction of 3D images in a sparse view angles Cone Beam CT (CBCT). For this reason, in the first phase, the 3D Radon space is generated using CBP data after discretization and optimization of the famous Grangeat’s formula. The method used in this process involves fast Pseudo Polar Fourier transform (PPFT) based on 2D and 3D Discrete Radon Transformation (DRT) algorithms with no wraparound effects. In the second phase, we describe reconstruction of the objects with available Radon values, using direct inverse of 3D PPFT. The method presented in this section eliminates noises caused by interpolation from polar to Cartesian space and exhibits no thorn, V-shaped and wrinkle artifacts. This method reduces the complexity to O(n3 log n) for images of size $ {{\mathrm {n}}\times {\mathrm {n}} \times {\mathrm {n}}}$. The Cone to Radon conversion (Cone2Radon) Toolbox in the first phase and MATLAB/Python toolbox in the second phase were tested on three digital phantoms and experiments demonstrate fast and accurate cone beam image reconstruction due to proposed modifications in all three stages of Grangeat’s method. [ABSTRACT FROM AUTHOR]

In this paper, we discuss about applications of different methods for decomposing a signal over elementary waveforms chosen in a family called a dictionary (atomic representations) in optical coherence tomography (OCT). If the representation is learned from the data, a nonparametric dictionary is defined with three fundamental properties of being data-driven, applicability on 3D, and working in multi-scale, which make it appropriate for processing of OCT images. We discuss about application of such representations including complex wavelet based K-SVD, and diffusion wavelets on OCT data. We introduce complex wavelet based K-SVD to take advantage of adaptability in dictionary learning methods to improve the performance of simple dual tree complex wavelets in speckle reduction of OCT datasets in 2D and 3D. The algorithm is evaluated on 144 randomly selected slices from twelve 3D OCTs taken by Topcon 3D OCT-1000 and Cirrus Zeiss Meditec. Improvement of contrast to noise ratio (CNR) (from 0.9 to 11.91 and from 3.09 to 88.9, respectively) is achieved. Furthermore, two approaches are proposed for image segmentation using diffusion. The first method is designing a competition between extended basis functions at each level and the second approach is defining a new distance for each level and clustering based on such distances. A combined algorithm, based on these two methods is then proposed for segmentation of retinal OCTs, which is able to localize 12 boundaries with unsigned border positioning error of 9.22 \pm 3.05 \mu \ m, on a test set of 20 slices selected from 13 3D OCTs. [ABSTRACT FROM AUTHOR]

This paper proposes a multimodal approach for vessel segmentation of macular optical coherence tomography (OCT) slices along with the fundus image. The method is comprised of two separate stages; the first step is 2-D segmentation of blood vessels in curvelet domain, enhanced by taking advantage of vessel information in crossing OCT slices (named feedback procedure), and improved by suppressing the false positives around the optic nerve head. The proposed method for vessel localization of OCT slices is also enhanced utilizing the fact that retinal nerve fiber layer becomes thicker in the presence of the blood vessels. The second stage of this method is axial localization of the vessels in OCT slices and 3-D reconstruction of the blood vessels. Twenty-four macular spectral 3-D OCT scans of 16 normal subjects were acquired using a Heidelberg HRA OCT scanner. Each dataset consisted of a scanning laser ophthalmoscopy (SLO) image and limited number of OCT scans with size of 496 × 512 (namely, for a data with 19 selected OCT slices, the whole data size was 496 × 512 × 19). The method is developed with least complicated algorithms and the results show considerable improvement in accuracy of vessel segmentation over similar methods to produce a local accuracy of 0.9632 in area of SLO, covered with OCT slices, and the overall accuracy of 0.9467 in the whole SLO image. The results are also demonstrative of a direct relation between the overall accuracy and percentage of SLO coverage by OCT slices. [ABSTRACT FROM PUBLISHER]