Learning the Sampling Pattern for MRI.

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 7 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling

High-Performance 3D Compressive Sensing MRI Reconstruction Using Many-Core Architectures

Compressive sensing (CS) describes how sparse signals can be accurately reconstructed from many fewer samples than required by the Nyquist criterion. Since MRI scan duration is proportional to the number of acquired samples, CS has been gaining significant attention in MRI. However, the computationally intensive nature of CS reconstructions has precluded their use in routine clinical practice. In this work, we investigate how different throughput-oriented architectures can benefit one CS algorithm and what levels of acceleration are feasible on different modern platforms. We demonstrate that a CUDA-based code running on an NVIDIA Tesla C2050 GPU can reconstruct a 256 × 160 × 80 volume from an 8-channel acquisition in 19 seconds, which is in itself a significant improvement over the state of the art. We then show that Intel's Knights Ferry can perform the same 3D MRI reconstruction in only 12 seconds, bringing CS methods even closer to clinical viability

Three-Dimensional Photoacoustic Computed Tomography: Imaging Models and Reconstruction Algorithms

Photoacoustic computed tomography: PACT), also known as optoacoustic tomography, is a rapidly emerging imaging modality that holds great promise for a wide range of biomedical imaging applications. Much effort has been devoted to the investigation of imaging physics and the optimization of experimental designs. Meanwhile, a variety of image reconstruction algorithms have been developed for the purpose of computed tomography. Most of these algorithms assume full knowledge of the acoustic pressure function on a measurement surface that either encloses the object or extends to infinity, which poses many difficulties for practical applications. To overcome these limitations, iterative image reconstruction algorithms have been actively investigated. However, little work has been conducted on imaging models that incorporate the characteristics of data acquisition systems. Moreover, when applying to experimental data, most studies simplify the inherent three-dimensional wave propagation as two-dimensional imaging models by introducing heuristic assumptions on the transducer responses and/or the object structures. One important reason is because three-dimensional image reconstruction is computationally burdensome. The inaccurate imaging models severely limit the performance of iterative image reconstruction algorithms in practice. In the dissertation, we propose a framework to construct imaging models that incorporate the characteristics of ultrasonic transducers. Based on the imaging models, we systematically investigate various iterative image reconstruction algorithms, including advanced algorithms that employ total variation-norm regularization. In order to accelerate three-dimensional image reconstruction, we develop parallel implementations on graphic processing units. In addition, we derive a fast Fourier-transform based analytical image reconstruction formula. By use of iterative image reconstruction algorithms based on the proposed imaging models, PACT imaging scanners can have a compact size while maintaining high spatial resolution. The research demonstrates, for the first time, the feasibility and advantages of iterative image reconstruction algorithms in three-dimensional PACT

Structure-preserving machine learning for inverse problems

Inverse problems naturally arise in many scientific settings, and the study of these problems has been crucial in the development of important technologies such as medical imaging. In inverse problems, the goal is to estimate an underlying ground truth u∗, typically an image, from corresponding measurements y, where u∗ and y are related by y = N(A(u∗)) (1) for some forward operator A and noise-generating process N (both of which are generally assumed to be known). Variational regularisation is a well-established approach that can be used to approximately solve inverse problems such as Problem (1). In this approach an image is reconstructed from measurements y by solving a minimisation problem such as uˆ = argmin d(A(u),y) +αJ(u). (2) While this approach has proven very successful, it generally requires the parts that make up the optimisation problem to be carefully chosen, and the optimisation problem may require considerable computational effort to solve. There is an active line of research into overcoming these issues using data-driven approaches, which aim to use multiple instances of data to inform a method that can be used on similar data. In this dissertation we investigate ways in which favourable properties of the variational regularisation approach can be combined with a data-driven approach to solving inverse problems. In the first chapter of the dissertation, we propose a bilevel optimisation framework that can be used to optimise sampling patterns and regularisation parameters for variational image reconstruction in accelerated magnetic resonance imaging. We use this framework to learn sampling patterns that result in better image reconstructions than standard random variable density sampling patterns that sample with the same rate. In the second chapter of the dissertation, we study the use of group symmetries in learned reconstruction methods for inverse problems. We show that group invariance of a functional implies that the corresponding proximal operator satisfies a group equivariance property. Applying this idea to model proximal operators as roto-translationally equivariant in an unrolled iterative reconstruction method, we show that reconstruction performance is more robust when tested on images in orientations not seen during training (compared to similar methods that model proximal operators to just be translationally equivariant) and that good methods can be learned with less training data. In the final chapter of the dissertation, we propose a ResNet-styled neural network architecture that is provably nonexpansive. This architecture can be thought of as composing discretisations of gradient flows along learnable convex potentials. Appealing to a classical result on the numerical integration of ODEs, we show that constraining the operator norms of the weight operators is sufficient to give nonexpansiveness, and additional analysis in the case that the numerical integrator is the forward Euler method shows that the neural network is an averaged operator. This guarantees that its fixed point iterations are convergent, and makes it a natural candidate for a learned denoiser in a Plug-and-Play approach to solving inverse problemsCantab Capital Institute for the Mathematics of Informatio

4-D Tomographic Inference: Application to SPECT and MR-driven PET

Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference

Image Reconstructions of Compressed Sensing MRI with Multichannel Data

Magnetic resonance imaging (MRI) provides high spatial resolution, high-quality of soft-tissue contrast, and multi-dimensional images. However, the speed of data acquisition limits potential applications. Compressed sensing (CS) theory allowing data being sampled at sub-Nyquist rate provides a possibility to accelerate the MRI scan time. Since most MRI scanners are currently equipped with multi-channel receiver systems, integrating CS with multi-channel systems can further shorten the scan time and also provide a better image quality. In this dissertation, we develop several techniques for integrating CS with parallel MRI. First, we propose a method which extends the reweighted l1 minimization to the CS-MRI with multi-channel data. The individual channel images are recovered according to the reweighted l1 minimization algorithm. Then, the final image is combined by the sum-of-squares method. Computer simulations show that the new method can improve the reconstruction quality at a slightly increased computation cost. Second, we propose a reconstruction approach using the ubiquitously available multi-core CPU to accelerate CS reconstructions of multiple channel data. CS reconstructions for phase array system using iterative l1 minimization are significantly time-consuming, where the computation complexity scales with the number of channels. The experimental results show that the reconstruction efficiency benefits significantly from parallelizing the CS reconstructions, and pipelining multi-channel data on multi-core processors. In our experiments, an additional speedup factor of 1.6 to 2.0 was achieved using the proposed method on a quad-core CPU. Finally, we present an efficient reconstruction method for high-dimensional CS MRI with a GPU platform to shorten the time of iterative computations. Data managements as well as the iterative algorithm are properly designed to meet the way of SIMD (single instruction/multiple data) parallelizations. For three-dimension multi-channel data, all slices along frequency encoding direction and multiple channels are highly parallelized and simultaneously processed within GPU. Generally, the runtime on GPU only requires 2.3 seconds for reconstructing a simulated 4-channel data with a volume size of 256×256×32. Comparing to 67 seconds using CPU, it achieves 28 faster with the proposed method. The rapid reconstruction algorithms demonstrated in this work are expected to help bring high dimensional, multichannel parallel CS MRI closer to clinical applications

Towards on-line plan adaptation of unified intensity-modulated arc therapy using a fast-direct aperture optimization algorithm

External beam radiotherapy (EBRT) plays a vital role in the treatment of cancer, with close to half of all cancer patients receiving EBRT at some point over their course of treatment. Although EBRT is a well-established form of treatment, there are a number of ways in which EBRT could still be improved in terms of quality and efficiency for treatment planning and radiation dose delivery. This thesis reports a series of improvements made to EBRT. First, we developed and evaluated a new treatment planning technique called unified intensity-modulated arc therapy (UIMAT) which combines the optimization and delivery of rotational volumetric modulated arc therapy (VMAT) and fixed-gantry intensity-modulated radiation therapy (IMRT). When retrospectively compared to clinical treatment plans using VMAT or IMRT alone, UIMAT plans reduced the dose to nearby critical structures by as much as 23% without compromising tumour volume coverage. The UIMAT plans were also more efficient to deliver. The reduction in normal tissue dose could help lower the probability of treatment-related toxicities, or alternatively could be used to improve tumour control probability, via dose escalation, while maintaining current dose limits for organs at risk. Second, we developed a new fast inverse direct aperture optimization (FIDAO) algorithm for IMRT, VMAT, and UIMAT treatment planning. FIDAO introduces modifications to the direct aperture optimization (DAO) process that help improve its computational efficiency. As demonstrated in several test cases, these modifications do not significantly impact the plan quality but reduced the DAO time by as much as 200-fold. If implemented with graphical processing units (GPUs), this project may allow for applications such as on-line treatment adaptation. Third, we investigated a method of acquiring tissue density information from cone-beam computed tomography (CBCT) datasets for on-line dose calculations, plan assessment, and potentially plan adaptation using FIDAO. This calibration technique accounts for patient-specific scattering conditions, demonstrated high dosimetric accuracy, and can be easily automated for on-line plan assessment. Collectively, these three projects will help reduce the normal tissue doses from EBRT, improve the planning and delivery efficiency, and pave the way for application like on-line plan assessment and adaptive radiotherapy in response to anatomical changes