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We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees-of-freedom of the BCS model is smaller than that of the low-rank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting \ell1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorize–minimize algorithm, which decouples the original criterion into three simpler subproblems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of K-SVD dictionary learning scheme. The use of the \ell1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the \ell0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis functions that can be reliably estimated is restricted by the available measurements. We also observe that the proposed scheme is more robust to local minima compared to K-SVD method, which relies on greedy sparse coding. Our phase transition experiments demonstrate that the BCS scheme provides much better recovery rates than classical Fourier-based CS schemes, while being only marginally worse than the dictionary aware setting. Since the overhead in additionally estimating the dictionary is low, this method can be very useful in dynamic magnetic resonance imaging applications, where the signal is not sparse in known dictionaries. We demonstrate the utility of the BCS scheme in accelerating contrast enhanced dynamic data. We observe superior reconstruction performance with the BCS scheme in comparison to existing low rank and compressed sensing schemes. [ABSTRACT FROM AUTHOR]

We introduce a novel algorithm to recover sparse and low-rank matrices from noisy and undersampled measurements. We pose the reconstruction as an optimization problem, where we minimize a linear combination of data consistency error, nonconvex spectral penalty, and nonconvex sparsity penalty. We majorize the nondifferentiable spectral and sparsity penalties in the criterion by quadratic expressions to realize an iterative three-step alternating minimization scheme. Since each of these steps can be evaluated either analytically or using fast schemes, we obtain a computationally efficient algorithm. We demonstrate the utility of the algorithm in the context of dynamic magnetic resonance imaging (MRI) reconstruction from sub-Nyquist sampled measurements. The results show a significant improvement in signal-to-noise ratio and image quality compared with classical dynamic imaging algorithms. We expect the proposed scheme to be useful in a range of applications including video restoration and multidimensional MRI. [ABSTRACT FROM PUBLISHER]

Task-based assessment of image quality in undersampled magnetic resonance imaging (MRI) using constraints is important because of the need to quantify the effect of the artifacts on task performance. Fluid-attenuated inversion recovery (FLAIR) images are used in detection of small metastases in the brain. In this work we carry out two-alternative forced choice (2-AFC) studies with a small signal known exactly (SKE) but with varying background for reconstructed FLAIR images from undersampled multi-coil data. Using a 4x undersampling and a total variation (TV) constraint we found that the human observer detection performance remained fairly constant for a broad range of values in the regularization parameter before decreasing at large values. Using the TV constraint did not improve task performance. The non- prewhitening eye (NPWE) observer and sparse difference-of-Gaussians (S-DOG) observer with internal noise were used to model human observer detection. The parameters for the NPWE and the internal noise for the S-DOG were chosen to match the average percent correct (PC) in 2-AFC studies for three observers using no regularization. The NPWE model observer tracked the performance of the human observers as the regularization was increased but slightly over-estimated the PC for large amounts of regularization. The S-DOG model observer with internal noise tracked human performace for all levels of regularization studied. To our knowledge this is the first time that model observers have been used to track human observer detection for undersampled MRI.

Recent work on blind compressed sensing (BCS) has shown that exploiting sparsity in dictionaries that are learnt directly from the data at hand can outperform compressed sensing (CS) that uses fixed dictionaries. A challenge with BCS however is the large computational complexity during its optimization, which limits its practical use in several MRI applications. In this paper, we propose a novel optimization algorithm that utilize variable splitting strategies to significantly improve the convergence speed of the BCS optimization. The splitting allows us to efficiently decouple the sparse coefficient, and dictionary update steps from the data fidelity term, resulting in subproblems that take closed form analytical solutions, which otherwise require slower iterative conjugate gradient algorithms. Through experiments on multi coil parametric MRI data, we demonstrate the superior performance of BCS over conventional CS schemes, while achieving convergence speed up factors of over 10 fold over the previously proposed implementation of the BCS algorithm.

Several algorithms that model the voxel time series as a sparse linear combination of basis functions in a fixed dictionary were introduced to recover dynamic MRI data from under sampled Fourier measurements. We have recently demonstrated that the joint estimation of dictionary basis and the sparse coefficients from the k-space data results in improved reconstructions. In this paper, we investigate the use of additional priors on the learned basis functions. Specifically, we assume the basis functions to be sparse in pre-specified transform or operator domains. Our experiments show that this constraint enables the suppression of noisy basis functions, thus further improving the quality of the reconstructions. We demonstrate the usefulness of the proposed method through various reconstruction examples.