An optimization approach to signal extraction from noisy multivariate data

We consider a problem of blind signal extraction from noisy multivariate data, in which each datum represents a system's response, observed under a particular experimental condition. Our prototype example is multipixel functional images of brain activity in response to a set of prescribed experimental stimuli. We present a novel multivariate analysis technique, which identifies the different activity patterns (signals) that are attributable to specific experimental conditions, without a priori knowledge about the signal or the noise characteristics. The extracted signals, which we term the generalized indicator functions, are optimal in the sense that they maximize a weighted difference between the signal variance and the noise variance. With an appropriate choice of the weighting parameter, the method returns a set of images whose signal-to-noise ratios satisfy some user-defined level of significance. We demonstrate the performance of our method in optical intrinsic signal imaging of cat cortical area 17. We find that the method performs effectively and robustly in all tested data, which include both real experimental data and numerically simulated data. The method of generalized indicator functions is related to canonical variate analysis, a multivariate analysis technique that directly solves for the maxima of the signal-to-noise ratio, but important theoretical and practical differences exist, which can make our method more appropriate in certain situations.