Example of our method on spinal cord in-vitro data using nuclear norm minimization and nonnegative matrix factorization. Left: Raw data, Middle: Denoised data, Right: Final estimate. Bottom row: Inferred spikes. The synchronized neurons share the same temporal component and result in a rank-1 matrix that is correctly identified from our rank penalized algorithm.

Application of our algorithm to a spinal cord neuron, in-vitro using the GCaMP6 calcium indicator. The neuron was stimulated with antidromic stimulation so the true spike times are known. Top row: Left: Raw data, Middle: Results using pixel-by-pixel denoising and SVD. Right: Results using our spatial approach and an AR(2) model for the calcium dynamics. Bottom row: True spikes (purple dots) spikes inferred with the plain method (blue) and spikes inferred with the spatial method (green). Our algorithm correctly identifies the location of the neuron and removes the clutter, and correctly estimates the spike times.

Application of our algorithm to in-vivo dendritic imaging data (layer 5, rodent barrel cortex).  First two panels: Raw and denoised data. Right 4 panels: 4 of the components extracted from our algorithm. The extracted spatial components correspond to specific dendritic structures that are successfully segmented from the total activity. Another example is shown below.

Application of our method in mouse V1 data, GCaMP6s. Top row left: Raw data and denoised. Top row right: Raw data and denoised (zoomed-in). Bottom rows: Spatiotemporal contributions of 18 components. The first two components correspond to time-varying background activity that is successfully separated from the contributions of the individual neurons.