High-Resolution Free-Breathing Quantitative First-Pass Perfusion Cardiac MR Using Dual-Echo Dixon With Spatio-Temporal Acceleration.

Introduction: To develop and test the feasibility of free-breathing (FB), high-resolution quantitative first-pass perfusion cardiac MR (FPP-CMR) using dual-echo Dixon (FOSTERS; Fat-water separation for mOtion-corrected Spatio-TEmporally accelerated myocardial peRfuSion). Materials and Methods: FOSTERS was performed in FB using a dual-saturation single-bolus acquisition with dual-echo Dixon and a dynamically variable Cartesian k-t undersampling (8-fold) approach, with low-rank and sparsity constrained reconstruction, to achieve high-resolution FPP-CMR images. FOSTERS also included automatic in-plane motion estimation and T 2 * correction to obtain quantitative myocardial blood flow (MBF) maps. High-resolution (1.6 x 1.6 mm2) FB FOSTERS was evaluated in eleven patients, during rest, against standard-resolution (2.6 x 2.6 mm2) 2-fold SENSE-accelerated breath-hold (BH) FPP-CMR. In addition, MBF was computed for FOSTERS and spatial wavelet-based compressed sensing (CS) reconstruction. Two cardiologists scored the image quality (IQ) of FOSTERS, CS, and standard BH FPP-CMR images using a 4-point scale (1-4, non-diagnostic - fully diagnostic). Results: FOSTERS produced high-quality images without dark-rim and with reduced motion-related artifacts, using an 8x accelerated FB acquisition. FOSTERS and standard BH FPP-CMR exhibited excellent IQ with an average score of 3.5 ± 0.6 and 3.4 ± 0.6 (no statistical difference, p > 0.05), respectively. CS images exhibited severe artifacts and high levels of noise, resulting in an average IQ score of 2.9 ± 0.5. MBF values obtained with FOSTERS presented a lower variance than those obtained with CS. Discussion: FOSTERS enabled high-resolution FB FPP-CMR with MBF quantification. Combining motion correction with a low-rank and sparsity-constrained reconstruction results in excellent image quality.

Phase diagram of matrix compressed sensing.

In the problem of matrix compressed sensing, we aim to recover a low-rank matrix from a few noisy linear measurements. In this contribution, we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model where the matrix to be recovered is a product of random matrices. The results that we obtain using the replica method describe the state evolution of the Parametric Bilinear Generalized Approximate Message Passing (P-BiG-AMP) algorithm, recently introduced in J. T. Parker and P. Schniter [IEEE J. Select. Top. Signal Process. 10, 795 (2016)1932-455310.1109/JSTSP.2016.2539123]. We show the existence of two different types of phase transition and their implications for the solvability of the problem, and we compare the results of our theoretical analysis to the numerical performance reached by P-BiG-AMP. Remarkably, the asymptotic replica equations for matrix compressed sensing are the same as those for a related but formally different problem of matrix factorization.

Multiple phases in modularity-based community detection.

Detecting communities in a network, based only on the adjacency matrix, is a problem of interest to several scientific disciplines. Recently, Zhang and Moore have introduced an algorithm [Proc. Natl. Acad. Sci. USA 111, 18144 (2014)], called mod-bp, that avoids overfitting the data by optimizing a weighted average of modularity (a popular goodness-of-fit measure in community detection) and entropy (i.e., number of configurations with a given modularity). The adjustment of the relative weight, the "temperature" of the model, is crucial for getting a correct result from mod-bp. In this work we study the many phase transitions that mod-bp may undergo by changing the two parameters of the algorithm: the temperature T and the maximum number of groups q. We introduce a new set of order parameters that allow us to determine the actual number of groups q̂, and we observe on both synthetic and real networks the existence of phases with any q̂∈{1,q}, which were unknown before. We discuss how to interpret the results of mod-bp and how to make the optimal choice for the problem of detecting significant communities.

Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques.

This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. On the sensor side, without a reference beam, the CCD camera provides only intensity measurements. Within this framework, this paper shows that the TM can still be retrieved, through signal processing techniques of phase retrieval. This is experimentally validated on three criteria : quality of prediction, distribution of singular values, and quality of focusing.