Paper:
Sparse space-time deconvolution for Calcium image analysis
We describe a unified formulation and algorithm to find an extremely sparse representation for Calcium image sequences in terms of cell locations, cell shapes, spike timings and impulse responses. Solution of a single optimization problem yields cell segmentations and activity estimates that are on par with the state of the art, without the need for heuristic pre-or postprocessing. Experiments on real and synthetic data demonstrate the viability of the proposed method.

Review:
Comments:This paper presents a complete method for calcium imaging analysis with few user-adjustable parameters.  This high-quality work is clearly written and significant to a large number of researchers working with calcium imaging data, and the chosen approach of simultaneously optimising all parameters of the analysis is original.  There are a few issues that the authors should address to finalise this work.Major issues:1) Why is the limit on the number of types of impulse responses also K, the number of cells?  More importantly, why do the authors choose only 2 impulses for the analysis?  It seems quite clear from Figure 5 that the two filters are the calcium indicator responses to one or multiple action potentials.  Either reducing the number of time points for impulses (i.e. reduce F) or increasing the number of possible impulses (increase L) would be wise in order to capture the range of actual impulses that are observed in the fluorescence response to the many action potentials that may occur in the 3 second long time window that is currently used.2) One of the key advantages of the proposed method is the apparent reduction in the amount of “fiddling” necessary to go from raw calcium imaging data to observed events in cells in known positions.  The authors admit “the price to pay for this elegance .. is a much higher computational cost” without going into detail.  If this method is to be useful to researchers besides the authors, a detailed quantification of this “price” is needed.  Can this method be run in a reasonable amount of time on a decent PC, or is a computational cluster required?  How much longer does this optimisation take compared to the other methods the authors test?3) Figure 5 is difficult to interpret.  First of all, the learned “truly sparse” representation cyan and magenta symbols are difficult to see even when zooming in digitally, and they appear on both left and right panels of traces even though the legend claims they are on the right. Additionally, how are there are what appear to be signals in the right panel in locations without symbols?  Lastly, this data appears to come from a paper in which cell-attached recordings were performed.  If at all possible, the best possible test would be to see whether the “truly sparse” impulse times match actual recorded action potentials. Of course, the cell-attached data in the cited paper is zoomed in tightly on the recorded neuron, so the analysis problem is much reduced, but if any other data were available along these lines, that could lead to a highly calibrated method that would be used by many researchers. Minor issues:Please do not capitalise Calcium imaging.Page 1 line 040 “only a fraction of neuron fires” should be “only a fraction of neurons fire”Page 3 line 137 It was unclear until nearly the end of the paper exactly what an “impulse” or “pattern” of activity would like, perhaps the authors could plot one of the filters from the final figure earlier on or give a more precise description at the first usage of the term.  The first mention of the length of these ‘patterns’ says “the number of taps or coefficients F that the learned impulse responses may have”.  What is meant by “taps” ?Page 3 line 139 “six .. parameters”  I count 5 (K,H,J,L,F) unless the authors are also counting the background smoothness parameter described in the next section.Page 5 line 258 typo “we disregards”Page 5 line 263 please italicise priori if also italicising “a”Page 7 line 356 typo “SSTD does as well the”  should be “as well as the”