Paper:
Robust Estimation of Neural Signals in Calcium Imaging
Calcium imaging is a prominent technology in neuroscience research which allows for simultaneous recording of large numbers of neurons in awake animals. Automated extraction of neurons and their temporal activity from imaging datasets is an important step in the path to producing neuroscience results. However, nearly all imaging datasets contain gross contaminating sources which could originate from the technology used, or the underlying biological tissue. Although past work has considered the effects of contamination under limited circumstances, there has not been a general framework treating contamination and its effects on the statistical estimation of calcium signals. In this work, we proceed in a new direction and propose to extract cells and their activity using robust statistical estimation. Using the theory of M-estimation, we derive a minimax optimal robust loss, and also find a simple and practical optimization routine for this loss with provably fast convergence. We use our proposed robust loss in a matrix factorization framework to extract the neurons and their temporal activity in calcium imaging datasets. We demonstrate the superiority of our robust estimation approach over existing methods on both simulated and real datasets.

Review:
This is an important and timely paper in the automated signal detection of calcium imaging of neurons.   The authors have developed a new methodology based on careful noise model and robust statistics.   The prevalence of calcium imaging experimental studies has increased interest in powerful analysis methods for understanding correlation of neuronal firing patterns, and this paper represents a strong advance in this direction.
The use of robust location estimator appears be a good approach, particularly given the magnitude of signal and noise variability and strong presence of ouliers in neuropil.  It is somewhat surprising that previous methods have not considered this.
The author's noise model as a superposition of positive sources and lower amplitude normal component is interesting and gives more statistical power in the analysis.  In equations (2) these components should be more explicitly labelled for readability.
The authors present a rigorously argument for the algorithms convergence rate which is fast. 
The authors present a nice comparison of their EXTRACT algorithm with two other approaches in actual manually labelled microendoscopic single-photon imaging data and show superior performance.  This section of the paper could be developed a little more carefully with more explicitly stated performance statistics,  although Figure 4 is well done.
In summary this is a very strong paper on a timely and important topic.  The availability of a code and how it might be deployed would be helpful.