Introduction to linear and nonlinear programming

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.

Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. In recent years, enormous progress has been made in the problem of denoising, a special case of an inverse problem where the forward model is an identity operator. Similarly, great progress has been made in improving model-based inversion when the forward model corresponds to complex physical measurements in applications such as X-ray CT, electron-microscopy, MRI, and ultrasound, to name just a few. However, combining state-of-the-art denoising algorithms (i.e., prior models) with state-of-the-art inversion methods (i.e., forward models) has been a challenge for many reasons. In this paper, we propose a flexible framework that allows state-of-the-art forward models of imaging systems to be matched with state-of-the-art priors or denoising models. This framework, which we term as Plug-and-Play priors, has the advantage that it dramatically simplifies software integration, and moreover, it allows state-of-the-art denoising methods that have no known formulation as an optimization problem to be used. We demonstrate with some simple examples how Plug-and-Play priors can be used to mix and match a wide variety of existing denoising models with a tomographic forward model, thus greatly expanding the range of possible problem solutions.

/pdf/plug-and-play-priors-for-model-based-reconstruction-51xolwckvh.pdf

Plug-and-Play priors for model based reconstruction

A framework for an iterative reconstruction algorithm is described which combines two or more of an ordered subset method, a preconditioner method, and a nested loop method. In one type of implementation a nested loop (NL) structure is employed where the inner loop sub-problems are solved using ordered subset (OS) methods. The inner loop may be solved using OS and a preconditioner method. In other implementations, the inner loop problems are created by augmented Lagrangian methods and then solved using OS method.

Accelerated iterative reconstruction

The present approach relates to the training of a machine learning algorithm for image generation and use of such a trained algorithm for image generation. Training the machine learning algorithm may involve using multiple images produced from a single set of tomographic projection or image data (such as a simple reconstruction and a computationally intensive reconstruction), where one image is the target image that exhibits the desired characteristics for the final result. The trained machine learning algorithm may be used to generate a final image corresponding to a computationally intensive algorithm from an input image generated using a less computationally intensive algorithm.

Image generation using machine learning

Methods and apparatus for statistical iterative reconstruction are provided. One method includes pre-processing acquired raw measurement data to modify the raw data measurement data and determining a change in a variance of the raw measurement data resulting from the modification to the raw measurement data during pre-processing. The method also includes reconstructing an image using the modified raw measurement data resulting from the pre-processing and the determined change in variance.

Method and apparatus for statistical iterative reconstruction

Emission computed tomography is widely applied in medical diagnostic imaging, especially to determine physiological function. The available set of measurements is, however, often in- complete and corrupted, and the quality of image reconstruction is enhanced by the computation of a statistically optimal estimate. Most formulations of the estimation problem use the Poisson model to measure fidelity to data. The intuitive appeal and operational sim- plicity of quadratic approximations to the Poisson log likelihood make them an attractive alternative, but they imply a potential loss of reconstruction quality which has not often been studied. This pa- per presents quantitative comparisons between the two models and shows that a judiciously chosen quadratic, as part of a short series of Newton-style steps, yields reconstructions nearly indistinguish- able from those under the exact Poisson model. © 2000 SPIE and IS&T. (S1017-9909(00)00502-X)

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Newton-style optimization for emission tomographic estimation

A method for performing reference normalization for an image created by an imaging system. The imaging system includes a radiation detector array with a right and left edge. The method includes receiving a projection dataset created by the imaging system in response to a varying x-ray tube current. The projection dataset includes a view and predicted fluxes are calculated for the set of reference channels within the view. A right set of reference channels are located proximate at the right edge of the detector array and a left set of reference channels are located proximate to the left edge of the detector array. The method also includes calculating average actual fluxes for the sets of reference channels. Based on the predicted reference fluxes and the average fluxes, a reference correction value for the view is determined. The correction value is applied for the reference correction of the view.

Jean-Baptiste Thibault

Papers

Accelerated iterative reconstruction

Image generation using machine learning

Method and apparatus for statistical iterative reconstruction

Newton-style optimization for emission tomographic estimation

Method, system and storage medium for reference normalization for blocked reference channels