This code can be used to estimate the locations of a stream of decaying exponentials, such as neural spikes in a calcium imaging recording, as described in this paper:

Béjar, Benjamín and Gavin Mischler. "A finite rate of innovation approach for the estimation of a stream of decaying exponentials." 2020 54th Asilomar Conference on Signals, Systems, and Computers, (2020): 1497-1501.

The model assumes the input signal to come from a stream of dirac delta functions convolved with a causal decaying exponential. Thus, the signal in continuous-time is of the form

The continuous-time signal is then corrupted with noise and sampled to create the input to the method. The method estimates the amplitudes and locations of the delta functions.

Estimating spike times and amplitudes from a signal can be done with the following code:

from spikeFRInder import estimate_tk_ak
output = estimate_tk_ak(signal, Fs, K, alpha_grid_ends)
tk_indices = output['tk_indices']
ak_hat = output['ak_hat']

The code includes descriptions of all parameters.

An application of this is in spike inference with calcium imaging signals. This can be achieved with the following code.

from spikeFRInder import sliding_window_predict
smoothed_estimate_histogram = sliding_window_predict(signal, Fs, K_full_signal_estimate)

The code includes descriptions of all parameters, including optional arguments which should be optimized. The smoothed estimate histogram can be thresholded to obtain more exact spike location estimates.

An example using a synthetic calcium signal can be found in example.ipynb.

The following figure demonstrates a thresholded output from a real calcium imaging trace.

The script crossval.py was used to generate Fig. 4 in the paper. We do not own the data, which must be downloaded using a CRCNS.org account, so it is not included in this repository.

The calcium signal preprocessing was done with a slightly modified version of the preprocessing done by Theis et al. Benchmarking spike rate inference in population calcium imaging. Thus, the code in c2s_preprocess_modified.py comes from their provided code, with only a minor change in the method of robust linear regression.

@INPROCEEDINGS{bejar2020finite,
  author={Béjar, Benjamín and Mischler, Gavin},
  booktitle={2020 54th Asilomar Conference on Signals, Systems, and Computers}, 
  title={A finite rate of innovation approach for the estimation of a stream of decaying exponentials}, 
  year={2020},
  volume={},
  number={},
  pages={1497-1501},
  doi={10.1109/IEEECONF51394.2020.9443495}}