An adaptive scaled mean square error (SMSE) filter using a Hopfield neural-network-based algorithm is presented. We show the development of the original SMSE filter from the minimum mean square error (MMSE) filter and the parametric mean square error (PMSE) filter, both of which suffer from the oversmooth phenomena. The SMSE filter is more efficient than the PMSE filter in terms of noise remova...

We consider the compressed sensing problem, where the object x0 ∈ R is to be recovered from incomplete measurements y = Ax0 + z; here the sensing matrix A is an n × N random matrix with iid Gaussian entries and n < N . A popular method of sparsity-promoting reconstruction is `-penalized least-squares reconstruction (aka LASSO, Basis Pursuit). It is currently popular to consider the strict spars...

We propose a new method for evaluating the mean square error (mse) of a possibly biased estimator 1̂ θ , or, rather, the class of estimators to which it belongs. The method uses confidence intervals c of a corresponding unbiased estimator θ̂ and makes its assessment based on the extent to which c includes 1̂ θ . The method does not require an estimate, implicit or explicit, of the bias of 1̂ θ , is...

1School of Business Administration, Southwestern University of Finance and Economics No. 555, Liutai Ave, Wenjiang Zone, Chengdu 611130, China 2Yangtze Normal University, No. 98, Julong Ave, Fuling Zone, Chongqing, 408100, China 3School of Management and Economics University of Electronic Science and Technology of China No. 2006, Xiyuan Ave, West Hi-Tech Zone, Chengdu 611731, China e-mail: koug...

The performance of the Constant Modulus Algorithm can su er because of the existence of local minimawith large Mean Squared Error(MSE). This paper presents a new way of obtaining the optimumMSE over all delays using a second equalizer under a mixed Constant Modulus and Cross Correlation Algorithm (CM-CCA). Proof of convergence is obtained for the noiseless case. Simulations demonstrate the pote...

We propose a simple and efficient method to compute the weighted mean square error for a biorthogonal M-channel wavelet coder for multidimensional signals. Indeed, biorthogonal filters weight the amount of quantization error which appears on the reconstructed output.We show that the mean square error of a reconstructed signal, resulting from the quantization errors of the M cosets provided by a...

We consider the compressed sensing problem, where the object x0 ∈ R is to be recovered from incomplete measurements y = Ax0 + z; here the sensing matrix A is an n × N random matrix with iid Gaussian entries and n < N . A popular method of sparsity-promoting reconstruction is `-penalized least-squares reconstruction (aka LASSO, Basis Pursuit). It is currently popular to consider the strict spars...

We derive a simple general parametric representation of the rate–distortion function of a memoryless source, where both the rate and the distortion are given by integrals whose integrands include the minimum mean square error (MMSE) of the distortion ∆ = d(X, Y ) based on the source symbol X , with respect to a certain joint distribution of these two random variables. At first glance, these rel...