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Multiphoton calcium fluorescence imaging has gained prominence as a valuable tool for the study of brain cells, but the corresponding analytical regimes remain rather naive. In this paper, we develop a statistical framework that facilitates principled quantitative analysis of multiphoton images. The proposed methods discriminate the stimulus-evoked response of a neuron from the background firing and image artifacts. We develop a harmonic regression model with colored noise, and estimate the model parameters with computationally efficient algorithms. We apply this model to in vivo characterization of cells from the ferret visual cortex. The results demonstrate substantially improved tuning curve fitting and image contrast.