10 research outputs found
Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting
In this work, we introduce a highly efficient algorithm to address the
nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix
factorization (NMF) with an additional underapproximation constraint. NMU
results are interesting as, compared to traditional NMF, they present
additional sparsity and part-based behavior, explaining unique data features.
To show these features in practice, we first present an application to the
analysis of climate data. We then present an NMU-based algorithm to robustly
fit multiple parametric models to a dataset. The proposed approach delivers
state-of-the-art results for the estimation of multiple fundamental matrices
and homographies, outperforming other alternatives in the literature and
exemplifying the use of efficient NMU computations
Multi-scale approaches for high-speed imaging and analysis of large neural populations
Progress in modern neuroscience critically depends on our ability to observe the activity of large neuronal populations with cellular spatial and high temporal resolution. However, two bottlenecks constrain efforts towards fast imaging of large populations. First, the resulting large video data is challenging to analyze. Second, there is an explicit tradeoff between imaging speed, signal-to-noise, and field of view: with current recording technology we cannot image very large neuronal populations with simultaneously high spatial and temporal resolution. Here we describe multi-scale approaches for alleviating both of these bottlenecks. First, we show that spatial and temporal decimation techniques based on simple local averaging provide order-of-magnitude speedups in spatiotemporally demixing calcium video data into estimates of single-cell neural activity. Second, once the shapes of individual neurons have been identified at fine scale (e.g., after an initial phase of conventional imaging with standard temporal and spatial resolution), we find that the spatial/temporal resolution tradeoff shifts dramatically: after demixing we can accurately recover denoised fluorescence traces and deconvolved neural activity of each individual neuron from coarse scale data that has been spatially decimated by an order of magnitude. This offers a cheap method for compressing this large video data, and also implies that it is possible to either speed up imaging significantly, or to “zoom out” by a corresponding factor to image order-of-magnitude larger neuronal populations with minimal loss in accuracy or temporal resolution