Ddenoising of a Positive Signal with White Gaussian Noise by Using Wavelet Transform

Given a noisy sampled at equispaced points with white noise, we consider problems where the signal to be recovered is known to be positive; for example, images, chemical spectra or other measurements of intensities. Shrinking noisy wavelet coefficients via thresholding offers very attractive alternatives to existing methods of recovering signals from noisy data. In this paper, we propose a method of recovering the original signal from a corrupted noisy signal, guaranteeing the recovered signal positive. We first obtain wavelet coefficients by thresholding, and use a nonlinear optimization to find the denoised signal which must be positive. Numerical examples are used to illustrate the performance of the proposed algorithm.