/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Image reconstruction is essential for imaging applications across the physical and life sciences, including optical and radar systems, magnetic resonance imaging, X-ray computed tomography, positron emission tomography, ultrasound imaging and radio astronomy. During image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the exact inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain, the composition of which depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. Here we present a unified framework for image reconstruction-automated transform by manifold approximation (AUTOMAP)-which recasts image reconstruction as a data-driven supervised learning task that allows a mapping between the sensor and the image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for various magnetic resonance imaging acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate that manifold learning during training results in sparse representations of domain transforms along low-dimensional data manifolds, and observe superior immunity to noise and a reduction in reconstruction artefacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate that AUTOMAP and other learned reconstruction approaches will accelerate the development of new acquisition strategies across imaging modalities.

Image reconstruction by domain-transform manifold learning

X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information nee...

https://www.tandfonline.com/doi/pdf/10.1179/1743280413Y.0000000023

Quantitative X-ray tomography

Multislice helical computed tomography scanning offers the advantages of faster acquisition and wide organ coverage for routine clinical diagnostic purposes. However, image reconstruction is faced with the challenges of three-dimensional cone-beam geometry, data completeness issues, and low dosage. Of all available reconstruction methods, statistical iterative reconstruction (IR) techniques appear particularly promising since they provide the flexibility of accurate physical noise modeling and geometric system description. In this paper, we present the application of Bayesian iterative algorithms to real 3D multislice helical data to demonstrate significant image quality improvement over conventional techniques. We also introduce a novel prior distribution designed to provide flexibility in its parameters to fine-tune image quality. Specifically, enhanced image resolution and lower noise have been achieved, concurrently with the reduction of helical cone-beam artifacts, as demonstrated by phantom studies. Clinical results also illustrate the capabilities of the algorithm on real patient data. Although computational load remains a significant challenge for practical development, superior image quality combined with advancements in computing technology make IR techniques a legitimate candidate for future clinical applications.

/pdf/a-three-dimensional-statistical-approach-to-improved-image-1jddsdidms.pdf

A three-dimensional statistical approach to improved image quality for multislice helical CT.

The authors present a Markov random field model which allows realistic edge modeling while providing stable maximum a posterior (MAP) solutions. The model, referred to as a generalized Gaussian Markov random field (GGMRF), is named for its similarity to the generalized Gaussian distribution used in robust detection and estimation. The model satisfies several desirable analytical and computational properties for map estimation, including continuous dependence of the estimate on the data, invariance of the character of solutions to scaling of data, and a solution which lies at the unique global minimum of the a posteriori log-likelihood function. The GGMRF is demonstrated to be useful for image reconstruction in low-dosage transmission tomography. >

/pdf/a-generalized-gaussian-image-model-for-edge-preserving-map-2hc5rqzhhd.pdf

A generalized Gaussian image model for edge-preserving MAP estimation

Recent applications of model-based iterative reconstruction (MBIR) algorithms to multislice helical CT reconstructions have shown that MBIR can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts However, high computational cost and long reconstruction times remain as a barrier to the use of MBIR in practical applications Among the various iterative methods that have been studied for MBIR, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed The NH-ICD algorithm has a mechanism that adaptively selects voxels for update First, a voxel selection criterion VSC determines the voxels in greatest need of update Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence In order to speed up each voxel update, we also propose a fast 1-D optimization algorithm that uses a quadratic substitute function to upper bound the local 1-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm We examine the performance of the proposed algorithm using several clinical data sets of various anatomy The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries

Fast Model-Based X-Ray CT Reconstruction Using Spatially Nonhomogeneous ICD Optimization

Markov random fields (MRFs) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters (sometimes referred to as hyperparameters) is difficult in practice for two reasons: (i) direct parameter estimation for MRFs is known to be mathematically and numerically challenging; (ii) parameters can not be directly estimated because the true image cross section is unavailable. We propose a computationally efficient scheme to address both these difficulties for a general class of MRF models, and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF). We derive methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, /spl sigma/, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p. We present a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization (EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve the parameter estimates when the simulations are terminated prior to convergence. Experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets.

/pdf/ml-parameter-estimation-for-markov-random-fields-with-4ly6vtqltw.pdf

ML parameter estimation for Markov random fields with applications to Bayesian tomography

Beam hardening is a well-known effect in X-ray CT scanning that is caused by the interaction of a broad polychromatic source spectrum with energy-dependent material attenuation. If the scanned object only consists of a single material, the beam hardening effect can be corrected by sinogram precorrection techniques. However, when multiple materials are present, it becomes much more difficult to fully compensate for this distortion; in general, the beam hardening can contribute to reconstruction artifacts such as cupping and streaking. In this paper, we present a novel model-based iterative reconstruction algorithm that incorporates beam hardening correction (MBIR-BHC). Unlike most correction algorithms, which require knowledge of the X-ray spectrum or mass attenuation functions, the MBIR-BHC algorithm works by simultaneously reconstructing the image and estimating the beam-hardening function. The method is based on the assumption that the object is formed by a combination of two distinct materials that can be separated based on their densities. We formulate a poly-energetic X-ray forward model using a polynomial function of two material projections: one for the low-density material and one for the high. We then develop an alternating minimization algorithm for jointly estimating the reconstructed image, the material segmentation, and the coefficients of the two component polynomial that models the beam-hardening function. With this approach, the spectrum and mass attenuation functions are not needed in advance, and the correction is adapted to the dataset being reconstructed. We examine the performance of the proposed algorithm using both simulated and real datasets. Results indicate that the MBIR-BHC algorithm significantly reduces several reconstruction artifacts without advanced knowledge of the X-ray spectrum and material properties.

A Model-Based Image Reconstruction Algorithm With Simultaneous Beam Hardening Correction for X-Ray CT

Over the past two decades, rapid system and hardware development of x-ray computed tomography (CT) technologies has been accompanied by equally exciting advances in image reconstruction algorithms. The algorithmic development can generally be classified into three major areas: analytical reconstruction, model-based iterative reconstruction, and application-specific reconstruction. Given the limited scope of this chapter, it is nearly impossible to cover every important development in this field; it is equally difficult to provide sufficient breadth and depth on each selected topic. As a compromise, we have decided, for a selected few topics, to provide sufficient high-level technical descriptions and to discuss their advantages and applications.

/pdf/recent-advances-in-ct-image-reconstruction-53gcrwhb8x.pdf

Ken D. Sauer

Papers

A three-dimensional statistical approach to improved image quality for multislice helical CT.

Fast Model-Based X-Ray CT Reconstruction Using Spatially Nonhomogeneous ICD Optimization

ML parameter estimation for Markov random fields with applications to Bayesian tomography

A Model-Based Image Reconstruction Algorithm With Simultaneous Beam Hardening Correction for X-Ray CT

Recent Advances in CT Image Reconstruction