We present a structured matrix factorization approach to analyzing calcium
imaging recordings of large neuronal ensembles. Our goal is to simultaneously
identify the locations of the neurons, demix spatially overlapping components,
and denoise and deconvolve the spiking activity of each neuron from the slow
dynamics of the calcium indicator. The matrix factorization approach relies on
the observation that the spatiotemporal fluorescence activity can be expressed
as a product of two matrices: a spatial matrix that encodes the location of
each neuron in the optical field and a temporal matrix that characterizes the
calcium concentration of each neuron over time. We present a simple approach
for estimating the dynamics of the calcium indicator as well as the observation
noise statistics from the observed data. These parameters are then used to set
up the matrix factorization problem in a constrained form that requires no
further parameter tuning. We discuss initialization and post-processing
techniques that enhance the performance of our method, along with efficient and
largely parallelizable algorithms. We apply our method to {\it in vivo} large
scale multi-neuronal imaging data and also demonstrate how similar methods can
be used for the analysis of {\it in vivo} dendritic imaging data.

本研究提出了一种结构化矩阵因数分解方法，用于同时解决大量神经元集合的位置识别，空间重叠组件混合分离以及每个神经元的钙离子浓度与时间关系的脉冲活动去噪和解卷积问题。