Two-photon laser-scanning microscopy has emerged as a powerful tool for in vivo functional imaging of the brain at the cellular and subcellular resolution. One prominent application is the estimation of neural coding properties from changes in somatic calcium, taken from time series imaging of tissue loaded with fluorescent calcium indicators. The true potential of this emerging modality for physiological imaging has not yet been achieved, primarily because the analysis methods developed so far are rather rudimentary. We present a new signal processing framework for two-photon imaging data that facilitates the statistical modeling of neuronal responses to the stimuli presented. We use a signal-plus-noise model for the measured calcium fluorescence, noting that the latter consists of the neuronal response corrupted by background activity and various sources of noise. A multiple harmonic regression approach is used to model the stimulus-evoked response (the signal component), while an autoregressive (AR) process is used to capture the stimulus-free response (the colored noise component). The joint estimation of signal and noise is achieved by a cyclic descent approach, making use of the Burg and Durbin-Levinson algorithms for the estimation of the AR parameters and the iterative covariance estimation. This approach helps us decompose an involved nonlinear estimation problem into two multivariate linear regression problems, yielding near-optimal estimates with high computational efficiency. The optimal model orders for the harmonic regression and AR models are determined by the Akaike information criterion and other related measures. A complete statistical description, including the confidence intervals and significance test results, are obtained for the model parameters and the signal and noise components. The decomposition of the data into these two distinct components not only offers insight into the underlying physiology but also leads us to obtain a principled estimate of the neuronal signal-to-noise ratio. We use this method to model the responses of neurons in the ferret primary visual cortex to visual stimuli varying periodically or episodically in the parameter of interest, such as orientation, direction of motion, spatial frequency or temporal frequency. The images reconstructed from our model applied to each pixel’s time series data have substantial contrast enhancement and noise rejection compared to conventional processing. The response tuning curve estimates are also significantly improved, enabling reliable inference of the functional characteristics of the imaged neurons.

Society for Neuroscience Abstract, 2009.