Recursive Nearest Agglomeration (ReNA): Fast Clustering for Approximation of Structured Signals.

In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure, such as with images. We focus on this setting and investigate feature clustering schemes for data reductions that capture this structure. An impediment to fast dimension reduction is then that good clustering comes with large algorithmic costs. We address it by contributing a linear-time agglomerative clustering scheme, Recursive Nearest Agglomeration (ReNA). Unlike existing fast agglomerative schemes, it avoids the creation of giant clusters. We empirically validate that it approximates the data as well as traditional variance-minimizing clustering schemes that have a quadratic complexity. In addition, we analyze signal approximation with feature clustering and show that it can remove noise, improving subsequent analysis steps. As a consequence, data reduction by clustering features with ReNA yields very fast and accurate models, enabling to process large datasets on budget. Our theoretical analysis is backed by extensive experiments on publicly-available data that illustrate the computation efficiency and the denoising properties of the resulting dimension reduction scheme.

A Projection Algorithm for Gradient Waveforms Design in Magnetic Resonance Imaging.

Collecting the maximal amount of information in a given scanning time is a major concern in magnetic resonance imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate, etc.), physical distortions (e.g., off-resonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g., spiral, radial lines, etc.) and then traversing it as fast as possible using optimal control. In this paper, we propose an alternative solution which first consists of defining a desired parameterization of the trajectory and then of optimizing for minimal deviation of the sampling points within gradient constraints. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. Third, it can be used both in the Shannon and CS sampling theories. Last, the optimized trajectory is computed as the solution of an efficient iterative algorithm based on convex programming. For piecewise linear trajectories, as compared to optimal control reparameterization, our approach generates a gain in scanning time of 10% in echo planar imaging while improving image quality in terms of signal-to-noise ratio (SNR) by more than 6 dB. We also investigate original trajectories relying on traveling salesman problem solutions. In this context, the sampling patterns obtained using the proposed projection algorithm are shown to provide significantly better reconstructions (more than 6 dB) while lasting the same scanning time.

Implementation of transportation distance for analyzing FLIM and FRET experiments.

Analysis of fluorescence lifetime imaging microscopy (FLIM) and Förster resonance energy transfer (FRET) experiments in living cells is usually based on mean lifetimes computations. However, these mean lifetimes can induce misinterpretations. We propose in this work the implementation of the transportation distance for FLIM and FRET experiments in vivo. This non-fitting indicator, which is easy to compute, reflects the similarity between two distributions and can be used for pixels clustering to improve the estimation of the FRET parameters. We study the robustness and the discriminating power of this transportation distance, both theoretically and numerically. In addition, a comparison study with the largely used mean lifetime differences is performed. We finally demonstrate practically the benefits of the transportation distance over the usual mean lifetime differences for both FLIM and FRET experiments in living cells.