11. Wavelet Transform in Remote Sensing with Implementation in Edge Detection and Noise Reduction

In image processing, the Fourier transform has a serious drawback as only frequency information remains whilst local information is lost. In order to involve localization in the analysis, the Short Time Fourier Transform (STFT) is adapted where the image is windowed. The drawback is that the window is the same in all frequencies. In principle, a more flexible approach is required where the window size varies in order to determine more precisely either location or frequency. Wavelet analysis allows the variation of the window based on the frequency information. Wavelets have limited duration and an average value of zero and thus they are irregular and asymmetric with short duration. Wavelets can be used in the field of edge detection and enhancement, image compression, noise reduction, and image fusion. In this review paper wavelets are used in quite opposite applications such as edge detection and noise reduction of remote sensing images. Thus, the flexibility and versatility of the wavelets is exposed. The challenge is to choose the appropriate wavelet for a particular application which is not known a priori.