Accelerated Cardiac Diffusion Tensor Imaging Using Joint Low-Rank and Sparsity Constraints

Objective: The purpose of this manuscript is to accelerate cardiac diffusion tensor imaging (CDTI) by integrating low-rankness and compressed sensing. Methods: Diffusion-weighted images exhibit both transform sparsity and low-rankness. These properties can jointly be exploited to accelerate CDTI, especially when a phase map is applied to correct for the phase inconsistency across diffusion directions, thereby enhancing low-rankness. The proposed method is evaluated both ex vivo and in vivo, and is compared to methods using either a low-rank or sparsity constraint alone. Results: Compared to using a low-rank or sparsity constraint alone, the proposed method preserves more accurate helix angle features, the transmural continuum across the myocardium wall, and mean diffusivity at higher acceleration, while yielding significantly lower bias and higher intraclass correlation coefficient. Conclusion: Low-rankness and compressed sensing together facilitate acceleration for both ex vivo and in vivo CDTI, improving reconstruction accuracy compared to employing either constraint alone. Significance: Compared to previous methods for accelerating CDTI, the proposed method has the potential to reach higher acceleration while preserving myofiber architecture features which may allow more spatial coverage, higher spatial resolution and shorter temporal footprint in the future.Comment: 11 pages, 16 figures, published on IEEE Transactions on Biomedical Engineerin

Accelerated parallel magnetic resonance imaging reconstruction using joint estimation with a sparse signal model

Accelerating magnetic resonance imaging (MRI) by reducing the number of acquired k-space scan lines benefits conventional MRI significantly by decreasing the time subjects remain in the magnet. In this paper, we formulate a novel method for Joint estimation from Undersampled LinEs in Parallel MRI (JULEP) that simultaneously calibrates the GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) reconstruction kernel and reconstructs the full multi-channel k-space. We employ a joint sparsity signal model for the channel images in conjunction with observation models for both the acquired data and GRAPPA reconstructed k-space. We demonstrate using real MRI data that JULEP outperforms conventional GRAPPA reconstruction at high levels of undersampling, increasing the peak-signal-to-noise ratio by up to 10 dB.National Science Foundation (U.S.) (CAREER Grant 0643836)National Center for Research Resources (U.S.) (P41 RR014075)National Institutes of Health (U.S.) (NIH R01 EB007942)National Institutes of Health (U.S.) (NIH R01 EB006847)Siemens CorporationNational Science Foundation (U.S.). Graduate Research Fellowship Progra

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

Successive Concave Sparsity Approximation for Compressed Sensing

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell_0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell_1$ and $\ell_0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed which leads to a number of weighted $\ell_1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.Comment: Submitted to IEEE Trans. on Signal Processin

Searching for structure in complex data: a modern statistical quest

Current research in statistics has taken interesting new directions, as data collected from scientific studies has become increasingly complex. At first glance, the number of experiments conducted by a scientist must be fairly large in order for a statistician to draw correct conclusions based on noisy measurements of a large number of factors. However, statisticians may often uncover simpler structure in the data, enabling accurate statistical inference based on relatively few experiments. In this snapshot, we will introduce the concept of high-dimensional statistical estimation via optimization, and illustrate this principle using an example from medical imaging. We will also present several open questions which are actively being studied by researchers in statistics

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Sparsity-Promoting Calibration for GRAPPA Accelerated Parallel MRI Reconstruction

The amount of calibration data needed to produce images of adequate quality can prevent auto-calibrating parallel imaging reconstruction methods like generalized autocalibrating partially parallel acquisitions (GRAPPA) from achieving a high total acceleration factor. To improve the quality of calibration when the number of auto-calibration signal (ACS) lines is restricted, we propose a sparsity-promoting regularized calibration method that finds a GRAPPA kernel consistent with the ACS fit equations that yields jointly sparse reconstructed coil channel images. Several experiments evaluate the performance of the proposed method relative to unregularized and existing regularized calibration methods for both low-quality and underdetermined fits from the ACS lines. These experiments demonstrate that the proposed method, like other regularization methods, is capable of mitigating noise amplification, and in addition, the proposed method is particularly effective at minimizing coherent aliasing artifacts caused by poor kernel calibration in real data. Using the proposed method, we can increase the total achievable acceleration while reducing degradation of the reconstructed image better than existing regularized calibration methods.National Science Foundation (U.S.) (CAREER Grant 0643836)National Institutes of Health (U.S.) (Grant NIH R01 EB007942)National Institutes of Health (U.S.) (Grant NIH R01 EB006847)National Institutes of Health (U.S.) (Grant NIH P41 RR014075)National Institutes of Health (U.S.) (Grant NIH K01 EB011498)National Institutes of Health (U.S.) (Grant NIH F32 EB015914)National Science Foundation (U.S.). Graduate Research Fellowship Progra

Acceleration of Subtractive Non-contrast-enhanced Magnetic Resonance Angiography

Although contrast-enhanced magnetic resonance angiography (CE-MRA) is widely established as a clinical examination for the diagnosis of human vascular diseases, non-contrast-enhanced MRA (NCE-MRA) techniques have drawn increasing attention in recent years. NCE-MRA is based on the intrinsic physical properties of blood and does not require the injection of any exogenous contrast agents. Subtractive NCE-MRA is a class of techniques that acquires two image sets with different vascular signal intensity, which are later subtracted to generate angiograms. The long acquisition time is an important drawback of NCE-MRA techniques, which not only limits the clinical acceptance of these techniques but also renders them sensitive to artefacts from patient motion. Another problem for subtractive NCE-MRA is the unwanted residual background signal caused by different static background signal levels on the two raw image sets. This thesis aims at improving subtractive NCE-MRA techniques by addressing both these limitations, with a particular focus on three-dimensional (3D) femoral artery fresh blood imaging (FBI). The structure of the thesis is as follows: Chapter 1 describes the anatomy and physiology of the vascular system, including the characteristics of arteries and veins, and the MR properties and flow characteristics of blood. These characteristics are the foundation of NCE-MRA technique development. Chapter 2 introduces commonly used diagnostic angiographic methods, particularly CE-MRA and NCE-MRA. Current NCE-MRA techniques are reviewed and categorised into different types. Their principles, implementations and limitations are summarised. Chapter 3 describes imaging acceleration theories including compressed sensing (CS), parallel imaging (PI) and partial Fourier (PF). The Split Bregman algorithm is described as an efficient CS reconstruction method. The SPIRiT reconstruction for PI and homodyne detection for PF are also introduced and combined with Split Bregman to form the basis of the reconstruction strategy for undersampled MR datasets. Four image quality metrics are presented for evaluating the quality of reconstructed images. In Chapter 4, an intensity correction method is proposed to improve background suppression for subtractive NCE-MRA techniques. Residual signals of background tissues are removed by performing a weighted subtraction, in which the weighting factor is obtained by a robust regression method. Image sparsity can also be increased and thereby potentially benefit CS reconstruction in the following chapters. Chapter 5 investigates the optimal k-space sampling patterns for the 3D accelerated femoral artery FBI sequence. A variable density Poisson-disk with a fully sampled centre region and missing partial Fourier fractions is employed for k-space undersampling in the ky-kz plane. Several key parameters in sampling pattern design, such as partial Fourier sampling ratios, fully sampled centre region size and density decay factor, are evaluated and optimised. Chapter 6 introduces several reconstruction strategies for accelerated subtractive NCE-MRA. A new reconstruction method, k-space subtraction with phase and intensity correction (KSPIC), is developed. By performing subtraction in k-space, KSPIC can exploit the sparsity of subtracted angiogram data and potentially improve the reconstruction performance. A phase correction procedure is used to restore the polarity of negative signals caused by subtraction. The intensity correction method proposed in Chapter 4 is also incorporated in KSPIC as it improves background suppression and thereby sparsity. The highly accelerated technique can be used not only to reduce the acquisition time, but also to enable imaging with increased resolution with no time penalty. A time-efficient high-resolution FBI technique is proposed in Chapter 7. By employing KSPIC and modifying the flow-compensation/spoiled gradients, the image matrix size can be increased from 256×256 to up to 512×512 without prolonging the acquisition time. Chapter 8 summarises the overall achievements and limitations of this thesis, as well as outlines potential future research directions.Cambridge Trust China Scholarship Council Addenbrooke’s Charitable Trust National Institute of Health Research, Cambridge Biomedical Research Cente