This is a Python implementation of Joshua Vogelstein's fast non-negative deconvolution algorithm for inferring spikes from neuronal calcium imaging data. Fast non-negative deconvolution uses an interior point method to solve the following optimization problem:

n_best = argmax_{n >= 0} P(n | F)

where n_best is the maximum a posteriori estimate for the most likely spike train, given the fluorescence signal F, and the model:

c_{t} = gamma*c_{t-1} + n_{t},                         n_{t} ~ Exponential(lambda*dt)
F_{p,t} = alpha_{p}*c_{t} + beta_{p} + epsilon_{p,t},  epsilon ~ N(0, sigma)

It is also possible to estimate the model parameters sigma, alpha, beta and lambda from the data using pseudo-EM updates.

This version was written for the Kaggle Connectomics Challenge, and was optimized for speed when dealing with very large arrays of fluorescence data. In particular, it wraps the dgtsv subroutine from the LAPACK Fortran library to efficiently solve for the update direction for each Newton step. The optional dependency on joblib allows multiple fluorescence traces to be processed in parallel.

• Big performance improvements for multi-pixel datasets. By pre-projecting the real fluorescence onto the estimated mask, the interior point algorithm operates only on 1D vectors over time, rather than 2D vectors over pixels and time
• Added an option to decimate the input array over time before initializing or updating the theta parameters. This is particularly useful for large multi-pixel datasets, where a lot of time is spent performing the least-squares fit to update the estimates of the mask and baseline.
• Removed some clutter and improved the clarity of some of the source code.

• numpy
• scipy
• matplotlib
• joblib - optional, required for parallel processing
• A shared LAPACK library (source is available from here; Ubuntu users can simply $ sudo apt-get install liblapack)

PyFNND has been tested on machines running Ubuntu Linux (14.04), and using numpy v1.8.1 and scipy v0.14.0, as well as the current bleeding-edge dev versions of both libraries. Comments, suggestions and bug reports are all welcome.

Install using pip:

$ pip install pyfnnd

Or from the root of the source distribution, simply call

$ python setup.py install

from pyfnnd import deconvolve, demo, plotting

# synthetic fluorescence movie
F, c, n, theta = demo.make_fake_movie(1000, dt=0.02, mask_shape=(64, 64),
                                      sigma=0.003, seed=0)

# deconvolve it, learning alpha, beta and lambda
n_best, c_best, LL, theta_best = deconvolve(
    F, dt=0.02, verbosity=1, learn_theta=(0, 1, 1, 1, 0),
    spikes_tol=1E-6, params_tol=1E-6
)

# plot the fit against the true parameters
plotting.ground_truth_2D(F, n_best, c_best, theta_best, n, c, theta, 0.02,
                         64, 64)

Vogelstein, J. T., Packer, A. M., Machado, T. a, Sippy, T., Babadi, B., Yuste, R., & Paninski, L. (2010). Fast nonnegative deconvolution for spike train inference from population calcium imaging. Journal of Neurophysiology, 104(6), 3691-704. doi:10.1152/jn.01073.2009

PyFNND is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.