14,501 research outputs found
Fast non-negative deconvolution for spike train inference from population calcium imaging
Calcium imaging for observing spiking activity from large populations of
neurons are quickly gaining popularity. While the raw data are fluorescence
movies, the underlying spike trains are of interest. This work presents a fast
non-negative deconvolution filter to infer the approximately most likely spike
train for each neuron, given the fluorescence observations. This algorithm
outperforms optimal linear deconvolution (Wiener filtering) on both simulated
and biological data. The performance gains come from restricting the inferred
spike trains to be positive (using an interior-point method), unlike the Wiener
filter. The algorithm is fast enough that even when imaging over 100 neurons,
inference can be performed on the set of all observed traces faster than
real-time. Performing optimal spatial filtering on the images further refines
the estimates. Importantly, all the parameters required to perform the
inference can be estimated using only the fluorescence data, obviating the need
to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure
Robust Kalman tracking and smoothing with propagating and non-propagating outliers
A common situation in filtering where classical Kalman filtering does not
perform particularly well is tracking in the presence of propagating outliers.
This calls for robustness understood in a distributional sense, i.e.; we
enlarge the distribution assumptions made in the ideal model by suitable
neighborhoods. Based on optimality results for distributional-robust Kalman
filtering from Ruckdeschel[01,10], we propose new robust recursive filters and
smoothers designed for this purpose as well as specialized versions for
non-propagating outliers. We apply these procedures in the context of a GPS
problem arising in the car industry. To better understand these filters, we
study their behavior at stylized outlier patterns (for which they are not
designed) and compare them to other approaches for the tracking problem.
Finally, in a simulation study we discuss efficiency of our procedures in
comparison to competitors.Comment: 27 pages, 12 figures, 2 table
Subsampling Algorithms for Semidefinite Programming
We derive a stochastic gradient algorithm for semidefinite optimization using
randomization techniques. The algorithm uses subsampling to reduce the
computational cost of each iteration and the subsampling ratio explicitly
controls granularity, i.e. the tradeoff between cost per iteration and total
number of iterations. Furthermore, the total computational cost is directly
proportional to the complexity (i.e. rank) of the solution. We study numerical
performance on some large-scale problems arising in statistical learning.Comment: Final version, to appear in Stochastic System
Impulsive noise removal from color images with morphological filtering
This paper deals with impulse noise removal from color images. The proposed
noise removal algorithm employs a novel approach with morphological filtering
for color image denoising; that is, detection of corrupted pixels and removal
of the detected noise by means of morphological filtering. With the help of
computer simulation we show that the proposed algorithm can effectively remove
impulse noise. The performance of the proposed algorithm is compared in terms
of image restoration metrics and processing speed with that of common
successful algorithms.Comment: The 6th international conference on analysis of images, social
networks, and texts (AIST 2017), 27-29 July, 2017, Moscow, Russi
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Review of Unbiased FIR Filters, Smoothers, and Predictors for Polynomial Signals
Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided
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