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

Markov random fields (MRFs) have been widely used as prior models in various inverse problems such as tomographic reconstruction. While MRFs provide a simple and often effective way to model the spatial dependencies in images, they suffer from the fact that parameter estimation is difficult. In practice, this means that MRFs typically have very simple structure that cannot completely capture the subtle characteristics of complex images. 
In this paper, we present a novel Gaussian mixture Markov random field model (GM-MRF) that can be used as a very expressive prior model for inverse problems such as denoising and reconstruction. The GM-MRF forms a global image model by merging together individual Gaussian-mixture models (GMMs) for image patches. In addition, we present a novel analytical framework for computing MAP estimates using the GM-MRF prior model through the construction of surrogate functions that result in a sequence of quadratic optimizations. We also introduce a simple but effective method to adjust the GM-MRF so as to control the sharpness in low- and high-contrast regions of the reconstruction separately. We demonstrate the value of the model with experiments including image denoising and low-dose CT reconstruction.

A Gaussian Mixture MRF for Model-Based Iterative Reconstruction with Applications to Low-Dose X-ray CT

A method for filtering a measurement of density of an object is described. The method includes filtering the measurement of the density and preserving a local average of the measurement and additional measurements when performing the filtering.

Systems and methods for filtering data in a medical imaging system

One of the most recent technological advancements in computed tomography (CT) is the introduction of multi-slice CT (MSCT). The state-of-the-art MSCT contains 16 detector rows and is capable of acquiring 16 projections simultaneously. In this paper, we propose a reconstruction algorithm that makes use of nontraditional reconstruction planes and convolution weighting. To minimize the impact of interpolation on slice-sensitivity-profile (SSP), conjugate samples are used for the projection interpolation. We use multiple convex planes as teh region of construction. This allows the generated weighting function to be smooth and differentiable. In addition, we make use of the fact that projections collected from a subset of detector rows are sufficient to perform a complete reconstruction. A convolution function is applied to the weighting function of each subset to minimize the impact of cone beam effects. The convolution function is chosen so that optimal balance is achieved between image artifact, slice-sensitivity-profile (SSP), and noise. Extensive phantom and clinical studies have been conducted to validate our approach. Our study indicates that compared to other row-interpolation based reconstruction algorithms, a 30% SSP improvement can be achieved with the proposed approach. In addition, image artifact suppression achieved with the proposed approach is on par or slightly better than the existing reconstruction algorithms. Extensive clinical studies have shown that the 16-slice scanner in conjugation with this algorithm produces nearly isotropic spatial resolution and allows much improved diagnostic image quality.

Convolution reconstruction algorithm for multi-slice helical CT

A method includes obtaining spectral computed tomography (CT) information via an acquisition unit having an X-ray source and a CT detector. The method also includes, generating, with one or more processing units, using at least one image transform, a first basis image and a second basis image using the spectral CT information. Further, the method includes performing, with the one or more processing units, guided processing on the second basis image using the first basis image as a guide to provide a modified second basis image. Also, the method includes performing at least one inverse image transform using the first basis image and the modified second basis image to generate at least one modified image.

Jean-Baptiste Thibault

Papers

A Gaussian Mixture MRF for Model-Based Iterative Reconstruction with Applications to Low-Dose X-ray CT

Systems and methods for filtering data in a medical imaging system

Convolution reconstruction algorithm for multi-slice helical CT

Systems and methods for guided de-noising for computed tomography

Imaging from Low‐intensity Data