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Fast online deconvolution of calcium imaging data
Fig 3
Optimizing sparsity parameter λ and AR coefficient 
.
(A) Running the active set method, with conservatively small estimate 
, yields an initial denoised estimate (blue) of the data (gray) roughly capturing the truth (red). We also report the correlation between the deconvolved estimate and true spike train as a direct measure for the accuracy of spike train inference. (B) Updating sparsity parameter λ according to Eq (18) such that RSS = σ2 T (left) shifts the current estimate downward (right, blue). (C) Running the active set method enforces the constraints again and is fast due to warm-starting. (D) Updating 
by minimizing the polynomial function RSS(
) and (E) running the warm-started active set method completes one iteration, which yields already a decent fit. (F) A few more iterations improve the solution further. The obtained estimate (blue) is hardly distinguishable from the one obtained with known true γ (yellow dashed trace, plotted in addition to the traces in A-E, is on top of blue solid line). Note that determining 
based on the autocovariance (additionally plotted purple trace) yields a crude solution that even misses spikes (at 24.6 s and 46.5 s).
doi: https://doi.org/10.1371/journal.pcbi.1005423.g003