Denoising for Improved Parametric MRI of the Kidney: Protocol for Nonlocal Means Filtering

In order to tackle the challenges caused by the variability in estimated MRI parameters (e.g., T2* and T2) due to low SNR a number of strategies can be followed. One approach is postprocessing of the acquired data with a filter. The basic idea is that MR images possess a local spatial structure that is characterized by equal, or at least similar, noise-free signal values in vicinities of a location. Then, local averaging of the signal reduces the noise component of the signal. In contrast, nonlocal means filtering defines the weights for averaging not only within the local vicinity, bur it compares the image intensities between all voxels to define “nonlocal” weights. Furthermore, it generally compares not only single-voxel intensities but small spatial patches of the data to better account for extended similar patterns. Here we describe how to use an open source NLM filter tool to denoise 2D MR image series of the kidney used for parametric mapping of the relaxation times T2* and T2.This chapter is based upon work from the COST Action PARENCHIMA, a community-driven network funded by the European Cooperation in Science and Technology (COST) program of the European Union, which aims to improve the reproducibility and standardization of renal MRI biomarkers.

Adaptive singular spectrum analysis for seismic denoising and interpolation

We have developed an adaptive singular spectrum analysis (ASSA) method for seismic data denoising and interpolation purposes. Our algorithm iteratively updates the singular-value decomposition (SVD) of current spatial patches using the most recently added spatial sample. The method reduces the computational cost of classic singular spectrum analysis (SSA) by requiring QR decompositions on smaller matrices rather than the factorization of the entire Hankel matrix of the data. A comparison between results obtained by the ASSA and SSA methods, in which the SVD applies to all of the traces at once, proves that the ASSA method is a valid way to cope with spatially varying dips. In addition, a comparison of the ASSA method with the windowed SSA method indicates gains in efficiency and accuracy. Synthetic and real data examples illustrate the effectiveness of our method.

EMERGING PROPERTIES IN POPULATION DYNAMICS WITH DIFFERENT TIME SCALES

The aim of this work is to show that at the population level, emerging properties may occur as a result of the coupling between the fast micro-dynamics and the slow macrodynamics. We studied a prey-predator system with different time scales in a heterogeneous environment. A fast time scale is associated to the migration process on spatial patches and a slow time scale is associated to the growth and the interactions between the species. Preys go on the spatial patches on which some resources are located and can be caught by the predators on them. The efficiency of the predators to catch preys is patch-dependent. Preys can be more easily caught on some spatial patches than others. Perturbation theory is used in order to aggregate the initial system of ordinary differential equations for the patch sub-populations into a macro-system of two differential equations governing the total populations. Firstly, we study the case of a linear process of migration for which the aggregated system is formally identical to the slow part of the full system. Then, we study an example of a nonlinear process of migration. We show that under these conditions emerging properties appear at the population level.