Decoding suprathreshold stochastic resonance with optimal weights

Adaptive recursive algorithm for optimal weighted suprathreshold stochastic resonance

“…In the case of stationary inputs, after successive iterations of the Kalman–LMS recursive algorithm it converges to the optimum Wiener solution in some statistical sense [ 24 ]. Our previous work [ 17 ] has shown that, for the case of identical thresholds, the optimal weighted decoding is equivalent to Wiener linear decoding. Therefore, for stationary inputs, the decoding performance exploiting Kalman–LMS recursive algorithm is consistent with that of optimal weighted decoding in the case of identical thresholds.…”

“…Here, the array sizes N =1, 3, 15 and 63 (from top to bottom), and the stationary input signal is Gaussian distributed. The circled red lines correspond to the MSE distortion for Kalman–LMS recursive algorithm, and the blue stars represent the MSE distortion for optimal weighted decoding presented in [ 17 ]. …”

“…Notably, although for the case of stationary inputs, the decoding performance of these two methods is equal under the condition of identical thresholds, the Kalman–LMS recursive algorithm is simple and generally easy to implement since the output weights are updated following each input signal sample, instead of calculating the output weights using all the training data in one shot. Therefore, compared with the optimal weighted decoding scheme [ 17 ], this Kalman–LMS recursive algorithm is a practical method for finding close approximate solutions to equation ( 2.10 ) in real time. Moreover, this Kalman–LMS recursive algorithm can adaptively adjust the weighting coefficients so as to minimize the MSE distortion without complete knowledge of input statistics and thus can be applicable to the non-stationary inputs and the coloured noise situations as shown in figures 2 and 3 – 6 (dashed lines).…”

“…Thus, such threshold systems can be described as stochastic signal quantizers that have been analysed in terms of lossy source coding and quantization theory [ 14 – 16 ]. Following the works in [ 14 – 16 ], we investigated the decoding scheme of quantized signal, named as optimal weighted decoding, by using weighted coefficients [ 17 , 18 ]. Our results show that under certain conditions the performance of the optimally weighted quantizer response is superior to that of the original unweighted arrays [ 17 , 18 ].…”

“…However, the previous studies [ 17 , 18 ] have been undertaken assuming that the input characteristics are statistically stationary, and the decoding schemes are based on a priori knowledge of the inputs. Specifically, the noise is modelled as white Gaussian distributed [ 17 , 18 ]. However, in practical applications, the statistical characteristics of the input signals are generally unknown or are often varied with time.…”