Image Reconstruction Image reconstruction by using local inverse for full field of view

The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact inverse from an approximate inverse with a few iterations. The IRM has been used in CT image reconstruction to lower the radiation dose. The IRM utilize the errors between the original measured data and the recalculated data to correct the reconstructed images. However if it is not smooth inside the object, there often is an over-correction along the boundary of the organs in the reconstructed images. The over-correction increase the noises especially on the edges inside the image. One solution to reduce the above mentioned noises is using some kind of filters. Filtering the noise before/after/between the image reconstruction processing. However filtering the noises also means reduce the resolution of the reconstructed images. The filtered image is often applied to the image automation for examples image segmentation or image registration but diagnosis. For diagnosis, doctor would prefer the original images without filtering process. In the time these authors of this manuscript did the work of interior image reconstruction with local inverse method, they noticed that the local inverse method does not only reduced the truncation artifacts but also reduced the artifacts and noise introduced from filtered back-projection method without truncation. This discovery lead them to develop the sub-regional iterative refinement (SIRM) image reconstruction method. The SIRM did good job to reduce the artifacts and noises in the reconstructed images. The SIRM divide the image to many small sub-regions. To each small sub-region the principle of local inverse method is applied.Comment: 39 pages, 9 figure

Fused Analytical and Iterative Reconstruction (AIR) via modified proximal forward-backward splitting: a FDK-based iterative image reconstruction example for CBCT

This work is to develop a general framework, namely analytical iterative reconstruction (AIR) method, to incorporate analytical reconstruction (AR) method into iterative reconstruction (IR) method, for enhanced CT image quality and reconstruction efficiency. Specifically, AIR is established based on the modified proximal forward-backward splitting (PFBS) algorithm, and its connection to the filtered data fidelity with sparsity regularization is discussed. As a result, AIR decouples data fidelity and image regularization with a two-step iterative scheme, during which an AR-projection step updates the filtered data fidelity term, while a denoising solver updates the sparsity regularization term. During the AR-projection step, the image is projected to the data domain to form the data residual, and then reconstructed by certain AR to a residual image which is then weighted together with previous image iterate to form next image iterate. Intuitively since the eigenvalues of AR-projection operator are close to the unity, PFBS based AIR has a fast convergence. Such an advantage is rigorously established through convergence analysis and numerical computation of convergence rate. The proposed AIR method is validated in the setting of circular cone-beam CT with AR being FDK and total-variation sparsity regularization, and has improved image quality from both AR and IR. For example, AIR has improved visual assessment and quantitative measurement in terms of both contrast and resolution, and reduced axial and half-fan artifacts

The Non-uniform Fast Fourier Transform in Computed Tomography

This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the potential computational efficiency which the Fourier Slice Theorem and the Non-uniform Fast Fourier Transform (NUFFT) will bring forth. In this Masters report, the detailed design of the NUFFT based forward projector including a novel 3D (derivative of) Radon space resampling method will be given. Meanwhile the complexity of the NUFFT based forward projector is analysed and compared with the non-Fourier based CT projector, and the advantage of the NUFFT based forward projection in terms of the computational efficiency is demonstrated in this report. Base on the design of the forward algorithm, the NUFFT based 3D direct reconstruction algorithm will be derived. The experiments will be taken to test the performance of the forward algorithm and the backprojection algorithm to show the practicability and accuracy of these designs by comparing them jointly with the well-acknowledged cone beam CT operators: the CT linear interpolation forward projector and the FDK algorithm. This Master report will demonstrate a novel and efficient way of implementing the cone beam CT operator, a detailed summary of the project, and the future research prospects of the NUFFT based cone beam CT algorithms.Comment: 50 pages. A Masters thesis achieved in the Institute of Digital Communications, the University of Edinburgh. Computer Science/Computation Complexit

RAPToR: A Resampling Algorithm for Pseudo-Polar based Tomographic Reconstruction

We propose a stable and fast reconstruction technique for parallel-beam (PB) tomographic X-ray imaging, relying on the discrete pseudo-polar (PP) Radon transform. Our main contribution is a resampling method, based on modern sampling theory, that transforms the acquired PB measurements to a PP grid. The resampling process is both fast and accurate, and in addition, simultaneously denoises the measurements, by exploiting geometrical properties of the tomographic scan. The transformed measurements are then reconstructed using an iterative solver with total variation (TV) regularization. We show that reconstructing from measurements on the PP grid, leads to improved recovery, due to the inherent stability and accuracy of the PP Radon transform, compared with the PB Radon transform. We also demonstrate recovery from a reduced number of PB acquisition angles, and high noise levels. Our approach is shown to achieve superior results over other state-of-the-art solutions, that operate directly on the given PB measurements. The proposed method can benefit fan-beam and/or cone-beam projections by coupling it with a rebinning process

Unsupervised Learnable Sinogram Inpainting Network (SIN) for Limited Angle CT reconstruction

In this paper, we propose a sinogram inpainting network (SIN) to solve limited-angle CT reconstruction problem, which is a very challenging ill-posed issue and of great interest for several clinical applications. A common approach to the problem is an iterative reconstruction algorithm with regularization term, which can suppress artifacts and improve image quality, but requires high computational cost. The starting point of this paper is the proof of inpainting function for limited-angle sinogram is continuous, which can be approached by neural networks in a data-driven method, granted by the universal approximation theorem. Based on this, we propose SIN as the fitting function -- a convolutional neural network trained to generate missing sinogram data conditioned on scanned data. Besides CNN module, we design two differentiable and rapid modules, Radon and Inverse Radon Transformer network, to encapsulate the physical model in the training procedure. They enable new joint loss functions to optimize both sinogram and reconstructed image in sync, which improved the image quality significantly. To tackle the labeled data bottleneck in clinical research, we form a sinogram-image-sinogram closed loop, and the difference between sinograms can be used as training loss. In this way, the proposed network can be self-trained, with only limited-angle data for unsupervised domain adaptation. We demonstrate the performance of our proposed network on parallel beam X-ray CT in lung CT datasets from Data Science Bowl 2017 and the ability of unsupervised transfer learning in Zubal's phantom. The proposed method performs better than state-of-art method SART-TV in PSNR and SSIM metrics, with noticeable visual improvements in reconstructions

Quantitative Study on Exact Reconstruction Sampling Condition in Limited-view CT

In limited-view computed tomography reconstruction, iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, inspired by compressive sensing, potentially claims large reductions in sampling requirements. However, a quantitative notion of this claim is non-trivial because of the ill-defined reduction in sampling achieved by the sparsity-exploiting method. In this paper, exact reconstruction sampling condition for limited-view problem is studied by verifying the uniqueness of solution in TV minimization model. Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness. Through this method, the sufficient sampling number of exact reconstruction is quantified for any fixed phantom and settled geometrical parameter in the limited-view problem. This paper provides a reference to quantify the sampling condition. Using Shepp-Logan phantom as an example, the experiment results show the quantified sampling number and indicate that an object would be accurately reconstructed as the scanning range becomes narrower by increasing sampling number. The increased samplings compensate for the deficiency of the projection angle. However, a lower bound of the scanning range is presented, in which an exact reconstruction cannot be obtained once the projection angle is narrowed to this extent no matter how to increase sampling

Non-local Low-rank Cube-based Tensor Factorization for Spectral CT Reconstruction

Spectral computed tomography (CT) reconstructs material-dependent attenuation images with the projections of multiple narrow energy windows, it is meaningful for material identification and decomposition. Unfortunately, the multi-energy projection dataset always contains strong complicated noise and result in the projections has a lower signal-noise-ratio (SNR). Very recently, the spatial-spectral cube matching frame (SSCMF) was proposed to explore the non-local spatial-spectrum similarities for spectral CT. The method constructs such a group by clustering up a series of non-local spatial-spectrum cubes. The small size of spatial patch for such a group make SSCMF fails to encode the sparsity and low-rank properties. In addition, the hard-thresholding and collaboration filtering operation in the SSCMF are also rough to recover the image features and spatial edges. While for all steps are operated on 4-D group, we may not afford such huge computational and memory load in practical. To avoid the above limitation and further improve image quality, we first formulate a non-local cube-based tensor instead of the group to encode the sparsity and low-rank properties. Then, as a new regularizer, Kronecker-Basis-Representation (KBR) tensor factorization is employed into a basic spectral CT reconstruction model to enhance the ability of extracting image features and protecting spatial edges, generating the non-local low-rank cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman strategy is adopted to solve the NLCTF model. Both numerical simulations and realistic preclinical mouse studies are performed to validate and assess the NLCTF algorithm. The results show that the NLCTF method outperforms the other competitors

Generalized-Equiangular Geometry CT: Concept and Shift-Invariant FBP Algorithms

With advanced X-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an X-ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs. GEGCT, unfortunately, has no theoretically exact and shift-invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in-depth investigation on a group of approximate Filtered BackProjection (FBP) algorithms with a variety of weighting strategies has been conducted. The architecture of GEGCT is first presented and characterized by using a normalized-radial-offset distance (NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a unified framework, with pre-filtering, filtering, and post-filtering weights. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. We further stretch the weighted FBP-type algorithms to GEGCT with dynamic NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in the case of cone-beam scan with a cylindrical detector array.Comment: 31 pages, 13 figure

BPF Algorithms for Multiple Source-Translation Computed Tomography Reconstruction

Micro-computed tomography (micro-CT) is a widely used state-of-the-art instrument employed to study the morphological structures of objects in various fields. Object-rotation is a classical scanning mode in micro-CT allowing data acquisition from different angles; however, its field-of-view (FOV) is primarily constrained by the size of the detector when aiming for high spatial resolution imaging. Recently, we introduced a novel scanning mode called multiple source translation CT (mSTCT), which effectively enlarges the FOV of the micro-CT system. Furthermore, we developed a virtual projection-based filtered backprojection (V-FBP) algorithm to address truncated projection, albeit with a trade-off in acquisition efficiency (high resolution reconstruction typically requires thousands of source samplings). In this paper, we present a new algorithm for mSTCT reconstruction, backprojection-filtration (BPF), which enables reconstructions of high-resolution images with a low source sampling ratio. Additionally, we found that implementing derivatives in BPF along different directions (source and detector) yields two distinct BPF algorithms (S-BPF and D-BPF), each with its own reconstruction performance characteristics. Through simulated and real experiments conducted in this paper, we demonstrate that achieving same high-resolution reconstructions, D-BPF can reduce source sampling by 75% compared with V-FBP. S-BPF shares similar characteristics with V-FBP, where the spatial resolution is primarily influenced by the source sampling.Comment: 22 pages, 12 figure

Improved Scatter Correction in X-Ray Cone Beam CT with Moving Beam Stop Array Using Johns' Equation

In this paper, an improved scatter correction with moving beam stop array (BSA) for x-ray cone beam (CB) CT is proposed. Firstly, correlation between neighboring CB views is deduced based on John's Equation. Then, correlation-based algorithm is presented to complement the incomplete views by using the redundancy (over-determined information) in CB projections. Finally, combining the algorithm with scatter correction method using moving BSA, where part of primary radiation is blocked and incomplete projections are acquired, an improved correction method is proposed. Effectiveness and robustness is validated by Monte Carlo (MC) simulation with EGSnrc on humanoid phantom.Comment: 4 pages, pp98-101, Proceedings of the 10th International Meeting on Fully Three-dimensional Image Reconstruction in Radiology and Nuclear Medicine, Beijing, China, 200