Multigrid Regularized Image Reconstruction for Limited-Data Tomography

In this paper, we developed an accelerated algorithm for the classical simultaneous iterative reconstruction technique (SIRT) method applied in CT image reconstruction. The proposed algorithm possesses the following two features. First, it can flexibly handle the image reconstruction problem where projection data is contaminated by Poisson noise. This property makes it successful in compensating the disadvantage of the typical algebraic reconstruction technique (ART) method. Second, we utilize Passty's proximal splitting framework to construct a row-action type accelerated iterative algorithm to minimize the cost function. The accelerating strategy makes it successful in compensating the disadvantage of the famous SIRT method. We proved that the new algorithm can achieve significant image quality with noise reduction in less than 10 iterations, while SIRT needs more than 200 iterations. Both digital phantom and clinical abdominal CT image were reconstructed for demonstrating the efficiency of the proposed method.

Gamma emission tomography (GET) detects fuel rods that emit gamma rays for potential use as verification tools in nuclear safeguards. In GET, iterative reconstruction algorithms are often used to reconstruct passive gamma-ray emitter source distributions. Generally, using noisy sinogram data, the iterative reconstruction algorithms increase the noise level on a reconstruction image with iterations. Thus, it is important to evaluate how performances of representative iterative reconstruction algorithms change with noisy sinogram data. The passive gamma-ray source distributions inside the mock-up of the water-water energetic reactor (WWER) fuel assembly having missing fuel rods were reconstructed by using the following algorithms: gradient method, steepest descent method, conjugate gradient reconstruction method, algebraic reconstruction technique, simultaneous iterative reconstruction technique, and maximum likelihood expectation maximization (MLEM). Consequently, MLEM algorithm yielded a higher contrast reconstruction image and was regarded as higher reliable algorithm to discriminate the fuel rods from the passive gamma-ray emitter source distribution.

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

To obtain useful knowledge and experience of CCERT under different excitation patterns, the image reconstruction performance of a 12-electrode CCERT sensor under five different excitation patterns (1-electrode excitation pattern, 2-electrode excitation pattern, 3-electrode excitation pattern, 4-electrode excitation pattern, and 5-electrode excitation pattern) are investigated and compared. A 12-electrode CCERT prototype, which can implement different excitation patterns, is developed to obtain the practical experiment data. Four typical image reconstruction algorithms (Linear Back Projection (LBP) algorithm, Landweber’s iteration algorithm, Algebraic Reconstruction Technique (ART) algorithm, and Simultaneous Iterative Reconstruction Technique (SIRT) algorithm) are introduced to investigate and compare the image reconstruction performance with the experimental data obtained from the CCERT prototype. Research results show that the 1-electrode excitation pattern and the 2-electrode excitation pattern have better global image reconstruction performance. These two excitation patterns are better choices, while the 3-electrode excitation pattern, the 4-electrode excitation pattern, and the 5-electrode excitation pattern are not recommended.

Algebraic Reconstruction Technique (ART) is an age-old method used for solving the problem of three-dimensional (3-D) reconstruction from projections in electron microscopy and radiology. In medical applications, direct 3-D reconstruction is at the forefront of investigation. The simultaneous iterative reconstruction technique (SIRT) is an ART-type algorithm with the potential of generating in a few iterations tomographic images of a quality comparable to that of convolution backprojection (CBP) methods. Pixel-based reconstruction (PBR) is similar to SIRT reconstruction, and it has been shown that PBR algorithms give better quality pictures compared to those produced by SIRT algorithms. In this work, we propose a few modifications to the PBR algorithms. The modified algorithms are shown to give better quality pictures compared to PBR algorithms. The PBR algorithm and the modified PBR algorithms are highly compute intensive, Not many attempts have been made to reconstruct objects in the true 3-D sense because of the high computational overhead. In this study, we have developed parallel two-dimensional (2-D) and 3-D reconstruction algorithms based on modified PBR. We attempt to solve the two problems encountered by the PBR and modified PBR algorithms, i.e., the long computational time and the large memory requirements, by parallelizing the algorithm on a multiprocessor system. We investigate the possible task and data partitioning schemes by exploiting the potential parallelism in the PBR algorithm subject to minimizing the memory requirement. We have implemented an extended hypercube (EH) architecture for the high-speed execution of the 3-D reconstruction algorithm using the commercially available fast floating point digital signal processor (DSP) chips as the processing elements (PEs) and dual-port random access memories (DPR) as channels between the PEs. We discuss and compare the performances of the PBR algorithm on an IBM 6000 RISC workstation, on a Silicon Graphics Indigo 2 workstation, and on an EH system. The results show that an EH(3,1) using DSP chips as PEs executes the modified PBR algorithm about 100 times faster than an LBM 6000 RISC workstation. We have executed the algorithms on a 4-node IBM SP2 parallel computer. The results show that execution time of the algorithm on an EH(3,1) is better than that of a 4-node IBM SP2 system. The speed-up of an EH(3,1) system with eight PEs and one network controller is approximately 7.85.

Three-dimensional maximum a posteriori (MAP) imaging with radiopharmaceuticals labeled with three Cu radionuclides

To investigate algebraic reconstruction technique (ART) for parallel imaging reconstruction of radial data, applied to accelerated cardiac cine. A graphics processing unit (GPU)-accelerated ART reconstruction was implemented and applied to simulations, point spread functions and in 12 subjects imaged with radial cardiac cine acquisitions. Cine images were reconstructed with radial ART at multiple undersampling levels (192 Nr × Np = 96 to 16). Images were qualitatively and quantitatively analyzed for sharpness and artifacts, and compared to filtered back-projection, and conjugate gradient SENSE. Radial ART provided reduced artifacts and mainly preserved spatial resolution, for both simulations and in vivo data. Artifacts were qualitatively and quantitatively less with ART than filtered back-projection using 48, 32, and 24 Np , although filtered back-projection provided quantitatively sharper images at undersampling levels of 48-24 Np (all P < 0.05). Use of undersampled radial data for generating auto-calibrated coil-sensitivity profiles resulted in slightly reduced quality. ART was comparable to conjugate gradient SENSE. GPU-acceleration increased ART reconstruction speed 15-fold, with little impact on the images. GPU-accelerated ART is an alternative approach to image reconstruction for parallel radial MR imaging, providing reduced artifacts while mainly maintaining sharpness compared to filtered back-projection, as shown by its first application in cardiac studies.

Emission tomography imaging modality has given a new dimension to the field of medicine and biology. The maximum a posteriori (MAP) and maximum likelihood (ML) algorithms are the widely used reconstruction algorithms for emission tomography. However, the images reconstructed by MAP and ML methods still suffer from artifacts such as noise, over-smoothing and streaking artifacts. These algorithms often fail to recognize the density class in the reconstruction and hence result in over penalization causing blurring effect. A good knowledge of prior distribution is a must for MAP-based method. Recently proposed median root prior (MRP) algorithm preserves the edges in the image, but the reconstructed image suffers from step like streaking artifact. In this work, a fuzzy logic based approach is proposed for the pixel-pixel nearest neighborhood interaction. The proposed algorithm consists of two elementary steps: (1) edge detection-fuzzy rule based derivatives are used for the detection of edges in the nearest neighborhood window; (2) fuzzy smoothing penalization is performed only for those pixels for which edges are missing in the neighborhood window. Analysis shows that the proposed fuzzy rule based reconstruction algorithm is capable of producing better estimates compared to the images reconstructed by MAP and MRP algorithms. The reconstructed images are sharper with small features being better resolved due to the nature of the fuzzy potential function.

Resolution in ART: An experimental investigation of the resolving power of an algebraic picture reconstruction technique

Super-resolution (SR) aims at generating a high resolution image or image sequence from several slightly different low-resolution images. In previous work, we have showed that a Maximum A Posteriori (MAP) SR algorithm can yield significant image quality enhancement of the individual respiratory gated PET frames. However, in the past it has been also argued that image-based motion correction algorithms yield sub-optimal results, particularly when images are reconstructed using iterative methods. Here, we evaluate the results incorporating MAP SR directly as part of the One-Step-Late (OSL) reconstruction algorithm. The evaluation used GATE simulated data. The IEC phantom with lesions between 10–37mm (contrast 8/1) was used to simulate 200 noise realizations of 6 frames, each shifted by 3mm along the z-axis relative to each other. The algorithm was also tested on four realistic phantoms. Gated respiratory images were reconstructed with the OPL-EM algorithm. Superresolution was performed through a MAP algorithm either as part of the reconstruction process or as a post-processing step applied to the individually reconstructed gated frames. A Huber prior was used as regularization term while the function yielded by the MAP method was optimized through a quasi-Newton algorithm. We compared signal-to-noise ratio (SNR) and contrast, as well as the bias-variance tradeoff for each algorithm. SR incorporated reconstruction led to 9% and 14% higher SNR and contrast respectively compared to the image-based SR. The bias-variance tradeoff showed that reconstruction-incorporated SR has a bias and variance of 39% lower and 60% higher respectively compared to image-based SR.

This paper presents a quantitative performance evaluation method for the maximum a posteriori (MAP) state estimate fusion algorithm. Under ideal conditions where data association is assumed to be perfect, it has been shown that the MAP or best linear unbiased estimate (BLUE) fusion formula provides the best linear minimum mean squared estimate (LMMSE) given local estimates under the linear Gaussian assumption for a static system. However, for a dynamic system where fusion is recursively performed by the fusion center on local estimates generated from local measurements, it is not obvious how the MAP algorithm will perform. In the past, several performance evaluation methods have been proposed for various fusion algorithms, including simple convex combination, cross-covariance combination, information matrix, and MAP fusion. However, not much has been done to quantify the steady state behavior of these fusion methods for a dynamic system. The goal of this work is to present analytical fusion performance results for MAP state estimate fusion without extensive Monte Carlo simulations, using an approach developed for steady state performance evaluation for track fusion. Two different communication strategies are considered: fusion with and without feedback to the sensors. Analytic curves for the steady state performance of the fusion algorithm for various communication patterns are presented under different operating conditions.

While high resolution, regularly gridded observations are generally preferred in remote sensing, actual observations are often not evenly sampled and have lower-than-desired resolution. Hence, there is an interest in resolution enhancement and image reconstruction. This paper discusses a general theory and techniques for image reconstruction and creating enhanced resolution images from irregularly sampled data. Using irregular sampling theory, we consider how the frequency content in aperture function-attenuated sidelobes can be recovered from oversampled data using reconstruction techniques, thus taking advantage of the high frequency content of measurements made with nonideal aperture filters. We show that with minor modification, the algebraic reconstruction technique (ART) is functionally equivalent to Grochenig's (1992) irregular sampling reconstruction algorithm. Using simple Monte Carlo simulations, we compare and contrast the performance of additive ART, multiplicative ART, and the scatterometer image reconstruction (SIR) (a derivative of multiplicative ART) algorithms with and without noise. The reconstruction theory and techniques have applications with a variety of sensors and can enable enhanced resolution image production from many nonimaging sensors. The technique is illustrated with ERS-2 and SeaWinds scatterometer data.

A comparison of algebraic reconstruction techniques for a single-detector muon computed tomography system

Optical projection tomography (OPT) is an advanced three-dimensional (3D) imaging technology, which uses the filtered backprojection (FBP) algorithm to recover the 3D volume with sufficient number of projections. As to in vivo imaging, it is urgent to reduce the number of projections because the acquisition time could be minimized. However, reconstructing from undersampled OPT data can lead to artifacts and the decline in image quality. The simultaneous iterative reconstruction technique (SIRT) is introduced to remove artifacts and improve the image quality. The image qualities reconstructed from FBP and SIRT separately are compared, and the structural similarity and peak signal-to-noise ratio are calculated. Through simulated phantoms and OPT data of in vivo zebrafish embryo, SIRT consistently outperforms FBP in terms of reduced artifacts and enhanced image contrast especially when the projection numbers are reduced. SIRT method can provide high-quality reconstruction with 50 or fewer projections, thereby significantly reducing the minimum acquisition time and light dose while maintaining reconstruction quality. Through optimization and GPU acceleration, the SIRT algorithm can converge faster so as to reduce the image processing time. To our knowledge, this is the first time one SIRT algorithm is used for reconstruction of sparse OPT data. The experimental results show that SIRT algorithm outperform FBP especially when the number of projections is reduced. In addition, SIRT performs better in the preservation of vascular signal, which is significant for the monitoring of angiogenesis.

The use of transmission electron tomography for three dimensional morphology analysis of nanostructured materials has grown significantly in recent years due to the improved robustness of automated image collection, alignment and reconstruction routines. Although the amount of published 3D electron tomography data has increased accordingly, in many cases the data is used purely for visualization purposes, due to the difficulty of making quantitative measurements from the as-reconstructed data. This is due to the traditionally difficult step of segmentation of the 3D image volume, which has been hindered due to noise, artifacts and lack of necessary image detail or sharpness. In this work the Simultaneous Iterative Reconstruction Technique (SIRT) is used to reconstruct High Angle Annular Dark Field-Scanning Transmission Electron Microscopy (HAADF-STEM) tomography data. The number of SIRT iterations is varied to optimize the reconstruction for segmentation. In particular, signal to noise ratio, signal to artifact ratio, and image blur are identified as parameters which each contribute to the suitability of the reconstruction for segmentation. The Expectation Maximization/ Maximization of Posterior Marginals image segmentation algorithm is applied to the SIRT reconstructions, and the resulting Average Intensity Projection (AIP) of the segmented image stack is compared to the raw tomography projection data.