Convolutional network denoising for acceleration of multi-shot diffusion MRI.

Multi-shot echo planar imaging is a promising technique to reduce geometric distortions and increase spatial resolution in diffusion-weighted MRI (DWI), at the expense of increased scan time. Moreover, performing DWI in the body requires multiple repetitions to obtain sufficient signal-to-noise ratio, which further increases the scan time. This work proposes to reduce the number of repetitions and perform denoising of high b-value images using a convolutional network denoising trained on single-shot DWI to accelerate the acquisition of multi-shot DWI. Convolutional network denoising is demonstrated to accelerate the acquisition of 2-shot DWI by a factor of 4 compared to the clinical standard on patients with rectal cancer. Image quality was evaluated using qualitative scores from expert body radiologists between accelerated and non-accelerated acquisition. Additionally, the effect of convolutional network denoising on each image quality score was analyzed using a Wilcoxon signed-rank test. Convolutional network denoising would enable to increase the number of shots without increasing scan time for significant geometric artifact reduction and spatial resolution increase.

Accelerated Diffusion-Weighted MRI of Rectal Cancer Using a Residual Convolutional Network.

This work presents a deep-learning-based denoising technique to accelerate the acquisition of high b-value diffusion-weighted MRI for rectal cancer. A denoising convolutional neural network (DCNN) with a combined L1-L2 loss function was developed to denoise high b-value diffusion-weighted MRI data acquired with fewer repetitions (NEX: number of excitations) using the low b-value image as an anatomical guide. DCNN was trained using 85 datasets acquired on patients with rectal cancer and tested on 20 different datasets with NEX = 1, 2, and 4, corresponding to acceleration factors of 16, 8, and 4, respectively. Image quality was assessed qualitatively by expert body radiologists. Reader 1 scored similar overall image quality between denoised images with NEX = 1 and NEX = 2, which were slightly lower than the reference. Reader 2 scored similar quality between NEX = 1 and the reference, while better quality for NEX = 2. Denoised images with fourfold acceleration (NEX = 4) received even higher scores than the reference, which is due in part to the effect of gas-related motion in the rectum, which affects longer acquisitions. The proposed deep learning denoising technique can enable eightfold acceleration with similar image quality (average image quality = 2.8 ± 0.5) and fourfold acceleration with higher image quality (3.0 ± 0.6) than the clinical standard (2.5 ± 0.8) for improved diagnosis of rectal cancer.

Quantum correlations for a simple kicked system with mixed phase space.

We investigate both the classical and quantum dynamics for a simple kicked system (the standard map) that classically has mixed phase space. For initial conditions in a portion of the chaotic region that is close enough to the regular region, the phenomenon of sticking leads to a power-law decay with time of the classical correlation function of a simple observable. Quantum mechanically, we find the same behavior, but with a smaller exponent. We consider various possible explanations of this phenomenon, and settle on a modification of the Meiss-Ott Markov tree model that takes into account quantum limitations on the flux through a turnstile between regions corresponding to states on the tree. Further work is needed to better understand the quantum behavior.

Universal exponent for transport in mixed Hamiltonian dynamics.

We compute universal distributions for the transition probabilities of a Markov model for transport in the mixed phase space of area-preserving maps and verify that the survival probability distribution for trajectories near an infinite island-around-island hierarchy exhibits, on average, a power-law decay with exponent γ=1.57. This exponent agrees with that found from simulations of the Hénon and Chirikov-Taylor maps. This provides evidence that the Meiss-Ott Markov tree model describes the transport for mixed systems.

Diffusion for ensembles of standard maps.

Two types of random evolution processes are studied for ensembles of the standard map with driving parameter K that determines its degree of stochasticity. For one type of process the parameter K is chosen at random from a Gaussian distribution and is then kept fixed, while for the other type it varies from step to step. In addition, noise that can be arbitrarily weak is added. The ensemble average and the average over noise of the diffusion coefficient are calculated for both types of processes. These two types of processes are relevant for two types of experimental situations as explained in the paper. Both types of processes destroy fine details of the dynamics, and the second process is found to be more effective in destroying the fine details. We hope that this work is a step in the efforts for developing a statistical theory for systems with mixed phase space (regular in some parts and chaotic in other parts).

Statistics of the island-around-island hierarchy in Hamiltonian phase space.

The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For area-preserving maps, this has been attributed to the stickiness of boundary circles, which separate chaotic and regular components. Though such dynamics has been extensively studied, a full understanding depends on many fine details that typically are beyond experimental and numerical resolution. This calls for a statistical approach, the subject of the present work. We calculate the statistics of the boundary circle winding numbers, contrasting the distribution of the elements of their continued fractions to that for uniformly selected irrationals. Since phase space transport is of great interest for dynamics, we compute the distributions of fluxes through island chains. Analytical fits show that the "level" and "class" distributions are distinct, and evidence for their universality is given.