Statistical mechanical assessment of a reconstruction limit of compressed sensing: Toward theoretical analysis of correlated signals

We provide a scheme for exploring the reconstruction limit of compressed sensing by minimizing the general cost function under the random measurement constraints for generic correlated signal sources. Our scheme is based on the statistical mechanical replica method for dealing with random systems. As a simple but non-trivial example, we apply the scheme to a sparse autoregressive model, where the first differences in the input signals of the correlated time series are sparse, and evaluate the critical compression rate for a perfect reconstruction. The results are in good agreement with a numerical experiment for a signal reconstruction.Comment: 6 pages, 3 figure

Statistical mechanical analysis of the Kronecker channel model for MIMO wireless communication

The Kronecker channel model of wireless communication is analyzed using statistical mechanics methods. In the model, spatial proximities among transmission/reception antennas are taken into account as certain correlation matrices, which generally yield non-trivial dependence among symbols to be estimated. This prevents accurate assessment of the communication performance by naively using a previously developed analytical scheme based on a matrix integration formula. In order to resolve this difficulty, we develop a formalism that can formally handle the correlations in Kronecker models based on the known scheme. Unfortunately, direct application of the developed scheme is, in general, practically difficult. However, the formalism is still useful, indicating that the effect of the correlations generally increase after the fourth order with respect to correlation strength. Therefore, the known analytical scheme offers a good approximation in performance evaluation when the correlation strength is sufficiently small. For a class of specific correlation, we show that the performance analysis can be mapped to the problem of one-dimensional spin systems in random fields, which can be investigated without approximation by the belief propagation algorithm

Generalization of generative model for neuronal ensemble inference method

Various brain functions that are necessary to maintain life activities materialize through the interaction of countless neurons. Therefore, it is important to analyze the structure of functional neuronal network. To elucidate the mechanism of brain function, many studies are being actively conducted on the structure of functional neuronal ensemble and hub, including all areas of neuroscience. In addition, recent study suggests that the existence of functional neuronal ensembles and hubs contributes to the efficiency of information processing. For these reasons, there is a demand for methods to infer functional neuronal ensembles from neuronal activity data, and methods based on Bayesian inference have been proposed. However, there is a problem in modeling the activity in Bayesian inference. The features of each neuron's activity have non-stationarity depending on physiological experimental conditions. As a result, the assumption of stationarity in Bayesian inference model impedes inference, which leads to destabilization of inference results and degradation of inference accuracy. In this study, we extend the range of the variable for expressing the neuronal state, and generalize the likelihood of the model for extended variables. By comparing with the previous study, our model can express the neuronal state in larger space. This generalization without restriction of the binary input enables us to perform soft clustering and apply the method to non-stationary neuroactivity data. In addition, for the effectiveness of the method, we apply the developed method to multiple synthetic fluorescence data generated from the electrical potential data in leaky integrated-and-fire model.Comment: 24 pages, 6 figure