Contents 1. Introduction
Suppose we observe a radar orthogonal complex signal at equispaced locations according to the model $$s_{n}=f(x_{n})+z_{n}, n=1,\cdots, N\eqno{\hbox{(1)}}$$ where the are identically and independently distributed standard complex Gaussian random variables. Therefore, we assume that the variance of the noise is known and unity Normal . In practice. the variance can be estimated by taking the median absolute deviation of the high level wavelet coefficients, as proposed in [1]. Our goal is to estimate with small mean-square-error (measured at the observation points), i.e. to find an estimate with risk: $$R(\hat{f}, f)={\sum\limits_{i=1}^{N}E\Vert\hat{f}(x_{i})-f({\rm x}_{i})\Vert_{2}^{2}\over N} \eqno{\hbox{(2)}}$$ where stands for the expectation over the observed noisy signal s. Waveshrink is an expansion-based nonparametric estimators proposed by Donoho and Johnstone [1] which assumes that the underlying complex signal can be well approximated by a linear combination of wavelets, namely, that , where the . are complex coefficients, and are complex wavelets.
