Calcium imaging has revolutionized systems neuroscience, providing the ability to image large neural populations with single-cell resolution. The resulting datasets are quite large (with scales of TB/hour in some cases), which has presented a barrier to routine open sharing of this data, slowing progress in reproducible research. State of the art methods for analyzing this data are based on nonnegative matrix factorization (NMF); these approaches solve a non-convex optimization problem, and are highly effective when good initializations are available, but can break down e.g. in low-SNR settings where common initialization approaches fail.Here we introduce an improved approach to compressing and denoising functional imaging data. The method is based on a spatially-localized penalized matrix decomposition (PMD) of the data to separate (low-dimensional) signal from (temporally-uncorrelated) noise. This approach can be applied in parallel on local spatial patches and is therefore highly scalable, does not impose nonnegativity constraints or require stringent identifiability assumptions (leading to significantly more robust results compared to NMF), and estimates all parameters directly from the data, so no hand-tuning is required. We have applied the method to a wide range of functional imaging data (including one-photon, two-photon, three-photon, widefield, somatic, axonal, dendritic, calcium, and voltage imaging datasets): in all cases, we observe ∼2-4x increases in SNR and compression rates of 20-300x with minimal visible loss of signal, with no adjustment of hyperparameters; this in turn facilitates the process of demixing the observed activity into contributions from individual neurons. We focus on two challenging applications: dendritic calcium imaging data and voltage imaging data in the context of optogenetic stimulation. In both cases, we show that our new approach leads to faster and much more robust extraction of activity from the video data.

No abstract

Abstract. Image nonlocal self-similarity has been widely adopted as natural image prior in various low-level vision tasks such as image restoration, while the low-rank matrix recovery theory has been drawing much attention to describe and utilize the image nonlocal self-similarities. However, whether the low-rank prior models exist to characterize the nonlocal self-similarity for a wide range of natural images is not clear yet. In this paper we investigate this issue by evaluating the heavy-tailed distributions of singular values of the matrices of nonlocal similar patches collected from natural images. A novel image prior model, namely nonlocal spectral prior (NSP) model, is then proposed to characterize the singular values of nonlocal similar patches. We consequently apply the NSP model to typical image restoration tasks, including denoising, superresolution and deblurring, and the experimental results demonstrated the highly competitive performance of NSP in solving these low-level vision problems.