Implementation of signal processing operations by transforms with random coefficients for neuronal systems modelling

This work investigates signal processing networks in which randomness is an inherent feature like in biological neuronal networks. Signal processing operations are usually performed with algorithms requiring high-precision and order. It is thus interesting to investigate how signal processing operations could be realized in systems with inherent randomness which is apparent in neuronal networks. We are studying possible implementation of convolution and correlation operations based on generalized transform approach with rectangular matrices generated by random sequences. Conditions are formulated and illustrated how correlation and convolution operators can be computed with such matrices. We show next that increasing the size of matrices allows to decrease the precision of operations and to introduce substantial quantization and thresholding. The use of random matrices provides also for strong robustness to noise resulting from unreliable operation. We show also that the nonlinearity due to the quantization and thresholding leads naturally to the decorrelation of transformation vectors which might be useful for associative storage.