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.

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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 system and method include acquisition of a set of image data corresponding to a time period of data acquisition, the set of image data corresponding to a plurality of voxels, wherein each of the plurality of voxels corresponds to a distinct acquisition time within the time period of data acquisition. The system and method further include the modeling of the plurality of voxels as a function of time based on a plurality of kinetic parameters associated therewith and reconstruction of an image from the set of image data based on the modeled plurality of voxels.

System and method of iterative image reconstruction for computed tomography

A mammography system includes a patient support with a breast opening. Beneath the patient support, an x-ray source transmits x-rays through a breast of a patient extending through the opening. An opposing x-ray detector receives the x-rays to obtain an x-ray image of the breast. The x-ray source and x-ray detector rotate around the opening while maintaining a fixed relation relative to one another, and a container is filled with a fluid and positioned proximate to and aligned with the opening to receive the breast. An ultrasound transmitter transmits sound waves through the breast when positioned within the fluid. An opposing ultrasound receiver receives the sound waves to obtain an ultrasound image of the breast. In a preferred embodiment, the mammography system positions the ultrasound transmitter and/or ultrasound receiver at a first position when obtaining the x-ray image of the breast and a second position when obtaining the ultrasound image of the breast. In other preferred embodiments, mammography methods correspond thereto.

Combining X-ray and ultrasound imaging for enhanced mammography

A method for correcting Positron Emission Tomography (PET) data includes adjusting a tube current generated by the CT imaging system to a second tube current value that is less than a first tube current value used to generate diagnostic quality CT images, and imaging the patient with the CT imaging system set at the second tube current value. The method also includes generating a plurality of computed tomography (CT) projection data from the CT imaging system and preprocessing the CT projection data to generate preprocessed CT projection data. The method further includes filtering the preprocessed CT projection data to reduce electronic noise to generate filtered CT projection data, and performing a minus logarithmic operation on the filtered CT projection data to generate the corrected PET data.

Method and apparatus for correcting multi-modality imaging data

A method for reconstructing image component densities of an object includes acquiring multi-spectral x-ray tomographic data, performing a material decomposition of the multi-spectral x-ray tomographic data to generate a plurality of material sinograms, and reconstructing a plurality of material component density images by iteratively optimizing a functional that includes a joint likelihood term of at least two of the material decomposed sinograms. An x-ray tomography imaging system and a non-transitory computer readable medium are also described herein.

Methods and systems for performing model-based iterative reconstruction

Some configurations of the present invention provide a method for reconstructing an image of an object of a computed tomographic imaging system having a detector array and a radiation source, wherein an arc of the detector array is not concentric to a focal spot of the radiation source. The method includes scanning the object with the computed tomographic imaging system to obtain a fan beam dataset, rebinning the fan beam dataset into a set of parallel datasets; and reconstructing an image utilizing the set of parallel datasets.

Jean-Baptiste Thibault

Papers

System and method of iterative image reconstruction for computed tomography

Combining X-ray and ultrasound imaging for enhanced mammography

Method and apparatus for correcting multi-modality imaging data

Methods and systems for performing model-based iterative reconstruction

Methods and apparatus for artifact reduction in computed tomography imaging systems