An optimization approach to signal extraction from noisy multivariate data

We consider a problem of blind signal extraction from noisy multivariate da ta, in which each datum represents a system's response, observed under a pa rticular experimental condition. Our prototype example is multipixel functi onal images of brain activity in response to a set of prescribed experiment al stimuli. We present a novel multivariate analysis technique, which ident ifies the different activity patterns (signals) that are attributable to sp ecific experimental conditions, without a priori knowledge about the signal or the noise characteristics. The extracted signals, which we term the gen eralized indicator functions, are optimal in the sense that they maximize a weighted difference between the signal variance and the noise variance. Wi th an appropriate choice of the weighting parameter, the method returns a s et of images whose signal-to-noise ratios satisfy some user-defined level o f significance. We demonstrate the performance of our method in optical int rinsic signal imaging of cat cortical area 17. We find that the method perf orms effectively and robustly in all tested data, which include both real e xperimental data and numerically simulated data. The method of generalized indicator functions is related to canonical variate analysis, a multivariat e analysis technique that directly solves for the maxima of the signal-to-n oise ratio, but important theoretical and practical differences exist, whic h can make our method more appropriate in certain situations. (C) 2001 Acad emic Press.