Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods

Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach taken in this thesis to speed up scan time, which is based on violating the Nyquist criterion by skipping measurements that would be normally acquired in a standard MRI procedure. The resulting problem can be classified in the general framework of linear ill-posed inverse problems. This thesis shows how low-dimensional signal models, specifically lowrank and sparsity, can help in the reconstruction of dynamic images from partial measurements. The use of these models are justified by significant developments in signal recovery techniques from partial data that have emerged in recent years in signal processing. The major contributions of this thesis are the development and characterisation of fast and efficient computational tools using convex low-rank and sparse constraints via proximal gradient methods, the development and characterisation of a novel joint reconstruction–separation method via the low-rank plus sparse matrix decomposition technique, and the development and characterisation of low-rank based recovery methods in the context of dynamic parallel MRI. Finally, an additional contribution of this thesis is to formulate the various MR image reconstruction problems in the context of convex optimisation to develop algorithms based on proximal splitting methods

Machine learning in Magnetic Resonance Imaging: Image reconstruction.

Magnetic Resonance Imaging (MRI) plays a vital role in diagnosis, management and monitoring of many diseases. However, it is an inherently slow imaging technique. Over the last 20 years, parallel imaging, temporal encoding and compressed sensing have enabled substantial speed-ups in the acquisition of MRI data, by accurately recovering missing lines of k-space data. However, clinical uptake of vastly accelerated acquisitions has been limited, in particular in compressed sensing, due to the time-consuming nature of the reconstructions and unnatural looking images. Following the success of machine learning in a wide range of imaging tasks, there has been a recent explosion in the use of machine learning in the field of MRI image reconstruction. A wide range of approaches have been proposed, which can be applied in k-space and/or image-space. Promising results have been demonstrated from a range of methods, enabling natural looking images and rapid computation. In this review article we summarize the current machine learning approaches used in MRI reconstruction, discuss their drawbacks, clinical applications, and current trends

Multi-modal Non-line-of-sight Passive Imaging

We consider the non-line-of-sight (NLOS) imaging of an object using the light reflected off a diffusive wall. The wall scatters incident light such that a lens is no longer useful to form an image. Instead, we exploit the 4D spatial coherence function to reconstruct a 2D projection of the obscured object. The approach is completely passive in the sense that no control over the light illuminating the object is assumed and is compatible with the partially coherent fields ubiquitous in both the indoor and outdoor environments. We formulate a multi-criteria convex optimization problem for reconstruction, which fuses the reflected field's intensity and spatial coherence information at different scales. Our formulation leverages established optics models of light propagation and scattering and exploits the sparsity common to many images in different bases. We also develop an algorithm based on the alternating direction method of multipliers to efficiently solve the convex program proposed. A means for analyzing the null space of the measurement matrices is provided as well as a means for weighting the contribution of individual measurements to the reconstruction. This paper holds promise to advance passive imaging in the challenging NLOS regimes in which the intensity does not necessarily retain distinguishable features and provides a framework for multi-modal information fusion for efficient scene reconstruction

Rekonstrukcija signala iz nepotpunih merenja sa primenom u ubrzanju algoritama za rekonstrukciju slike magnetne rezonance

In dissertation a problem of reconstruction of images from undersampled measurements is considered which has direct application in creation of magnetic resonance images. The topic of the research is proposition of new regularization based methods for image reconstruction which are based on statistical Markov random field models and theory of compressive sensing. With the proposed signal model which follows the statistics of images, a new regularization functions are defined and four methods for reconstruction of magnetic resonance images are derived.У докторској дисертацији разматран је проблем реконструкције сигнала слике из непотпуних мерења који има директну примену у креирању слика магнетне резнонаце. Предмет истраживања је везан за предлог нових регуларизационих метода реконструкције коришћењем статистичких модела Марковљевог случајног поља и теорије ретке репрезентације сигнала. На основу предложеног модела који на веродостојан начин репрезентује статистику сигнала слике предложене су регуларизационе функције и креирана четири алгоритма за реконструкцију слике магнетне резонанце.U doktorskoj disertaciji razmatran je problem rekonstrukcije signala slike iz nepotpunih merenja koji ima direktnu primenu u kreiranju slika magnetne reznonace. Predmet istraživanja je vezan za predlog novih regularizacionih metoda rekonstrukcije korišćenjem statističkih modela Markovljevog slučajnog polja i teorije retke reprezentacije signala. Na osnovu predloženog modela koji na verodostojan način reprezentuje statistiku signala slike predložene su regularizacione funkcije i kreirana četiri algoritma za rekonstrukciju slike magnetne rezonance

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

MR image reconstruction using deep density priors

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimationComment: Published in IEEE TMI. Main text and supplementary material, 19 pages tota