MIXANDMIX: numerical techniques for the computation of empirical spectral distributions of population mixtures

The MIXANDMIX (mixtures by Anderson mixing) tool for the computation of the empirical spectral distribution of random matrices generated by mixtures of populations is described. Within the population mixture model the mapping between the population distributions and the limiting spectral distribution can be obtained by solving a set of systems of non-linear equations, for which an efficient implementation is provided. The contributions include a method for accelerated fixed point convergence, a homotopy continuation strategy to prevent convergence to non-admissible solutions, a blind non-uniform grid construction for effective distribution support detection and approximation, and a parallel computing architecture. Comparisons are performed with available packages for the single population case and with results obtained by simulation for the more general model implemented here. Results show competitive performance and improved flexibility.Comment: 17 pages, 6 figure

Complex diffusion-weighted image estimation via matrix recovery under general noise models

We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity encoding reconstruction, where asymptotically optimal signal recovery guarantees can be attained by modeling the noise propagation in the reconstruction and subsequently simulating or calculating the limit singular value spectrum. Simple strategies are presented to deal with phase inconsistencies and optimize patch construction. The pertinence of our contributions is quantitatively validated on synthetic data, an in vivo adult example, and challenging neonatal and fetal cohorts. Our methodology is compared with related approaches, which generally operate on magnitude-only data and use data-based noise level estimation and singular value truncation. Visual examples are provided to illustrate effectiveness in generating denoised and debiased diffusion estimates with well preserved spatial and diffusion detail.Comment: 26 pages, 9 figure

Non-Rigid Groupwise Registration for Motion Estimation and Compensation in Compressed Sensing Reconstruc- tion of Breath-Hold Cardiac Cine MRI

Purpose: Compressed sensing methods with motion estimation and compensation techniques have been proposed for the reconstruction of accelerated dynamic MRI. However, artifacts that naturally arise in compressed sensing reconstruction procedures hinder the estimation of motion from reconstructed images, especially at high acceleration factors. This work introduces a robust groupwise non-rigid motion estimation technique applied to the compressed sensing reconstruction of dynamic cardiac cine MRI sequences. Theory and Methods: A spatio-temporal regularized, groupwise, non-rigid registration method based on a B-splines deformation model and a least squares metric is used to estimate and to compensate the movement of the heart in breath-hold cine acquisitions and to obtain a quasi-static sequence with highly sparse representation in temporally transformed domains. Results: Short axis in vivo datasets are used for validation, both original multi-coil as well as DICOM data. Fully sampled data were retrospectively undersampled with various acceleration factors and reconstructions were compared with the two well-known methods k-t FOCUSS and MASTeR. The proposed method achieves higher signal to error ratio and structure similarity index for medium to high acceleration factors. Conclusions: Reconstruction methods based on groupwise registration show higher quality recon- structions for cardiac cine images than the pairwise counterparts tested

Multi-Oriented Windowed Harmonic Phase Reconstruction for Robust Cardiac Strain Imaging

The purpose of this work is to develop a method for direct estimation of the cardiac strain tensor by extending the harmonic phase reconstruction on tagged magnetic resonance images to obtain more precise and robust measurements. The extension relies on the reconstruction of the local phase of the image by means of the windowed Fourier transform and the acquisition of an overdetermined set of stripe orientations in order to avoid the phase interferences from structures outside the myocardium and the instabilities arising from the application of a gradient operator. Results have shown that increasing the number of acquired orientations provides a signi cant improvement in the reproducibility of the strain measurements and that the acquisition of an extended set of orientations also improves the reproducibility when compared with acquiring repeated samples from a smaller set of orientations. Additionally, biases in local phase estimation when using the original harmonic phase formulation are greatly diminished by the one here proposed. The ideas here presented allow the design of new methods for motion sensitive magnetic resonance imaging, which could simultaneously improve the resolution, robustness and accuracy of motion estimates

Autocalibrated cardiac tissue phase mapping with multiband imaging and k-t acceleration

PURPOSE: To develop an autocalibrated multiband (MB) CAIPIRINHA acquisition scheme with in-plane k-t acceleration enabling multislice three-directional tissue phase mapping in one breath-hold. METHODS: A k-t undersampling scheme was integrated into a time-resolved electrocardiographic-triggered autocalibrated MB gradient-echo sequence. The sequence was used to acquire data on 4 healthy volunteers with MB factors of two (MB2) and three (MB3), which were reconstructed using a joint reconstruction algorithm that tackles both k-t and MB acceleration. Forward simulations of the imaging process were used to tune the reconstruction model hyperparameters. Direct comparisons between MB and single-band tissue phase-mapping measurements were performed. RESULTS: Simulations showed that the velocities could be accurately reproduced with MB2 k-t (average ± twice the SD of the RMS error of 0.08 ± 0.22 cm/s and velocity peak reduction of 1.03% ± 6.47% compared with fully sampled velocities), whereas acceptable results were obtained with MB3 k-t (RMS error of 0.13 ± 0.58 cm/s and peak reduction of 2.21% ± 13.45%). When applied to tissue phase-mapping data, the proposed technique allowed three-directional velocity encoding to be simultaneously acquired at two/three slices in a single breath-hold of 18 heartbeats. No statistically significant differences were detected between MB2/MB3 k-t and single-band k-t motion traces averaged over the myocardium. Regional differences were found, however, when using the American Heart Association model for segmentation. CONCLUSION: An autocalibrated MB k-t acquisition / reconstruction framework is presented that allows three-directional velocity encoding of the myocardial velocities at multiple slices in one breath-hold