ABSTRACT
This chapter describes of the several applications of wavelet transforms, only three well-known applications. These are: signal denoising, image compression, and wavelet neural networks. The chapter explores the possibility of using wavelets to remove noise from a signal. Actually, orthogonal transforms, including wavelet transforms, can be used for signal denoising. Nevertheless, wavelet transforms have been found to be good candidates for signal denoising in practice. The denoising is performed by first computing the discrete wavelet transform of the noisy signal. Then the coefficients are subject to some thresholding operation to remove the coefficients with small magnitude, and finally the coefficients are subject to inverse transform. A noise-contaminated signal is transformed via a discrete wavelet transform. Then the transformed coefficients are mapped according to a thresholding operator. An image can mathematically be considered as a function which takes nonnegative values on a plane. The reconstruction of the image from the coefficients proceeds as in the case of the one-dimensional wavelets.
