The processing of remotely sensed data includes compression, noise reduction, classification, feature extraction, change detection and any improvement associated with the problems at hand. In the literature, wavelet methods have been widely used for analysing remote sensing images and signals. The second-generation of wavelets, which is designed based on a method called the lifting scheme, is almost a new version of wavelets, and its application in the remote sensing field is fresh. Although first-generation wavelets have been proven to offer effective techniques for processing remotely sensed data, second-generation wavelets are more efficient in some respects, as will be discussed later. The aim of this review paper is to examine all existing studies in the literature related to applying second-generation wavelets for denoising remote sensing data. However, to make a better understanding of the application of wavelet-based denoising methods for remote sensing data, some studies that apply first-generation wavelets are also presented. In the part of hyperspectral data, there is a focus on noise removal from vegetation spectrum.
Hyperspectral vegetation spectrum is normally contaminated with noise and the presence of noise affects the results of vegetation studies, such as species discrimination and classification, disease detection, stress assessment and the estimation of vegetation's biophysical and biochemical characteristics. Additionally, hyperspectral signals are usually studied using the derivative analysis method that is very sensitive to noise in the data. This study investigates denoising of the hyperspectral vegetation spectrum using different waveletbased methods. A test signal and several real-world vegetation spectra are denoised using four wavelet methods: traditional discrete wavelet transform (DWT); stationary wavelet transform (SWT); lifting wavelet transform (LWT); and a combination of SWT and LWT, which in this paper is called stationary lifting wavelet transform (SLWT). SLWT incorporates the advantages of both SWT and LWT methods, including a translation invariance property and a fast simple algorithm. Experimental results show that SLWT highly outperforms other wavelet-based methods in terms of accuracy and visual quality. Furthermore, this research reveals the following novel results: SLWT 1) for different levels of decomposition of the wavelet transform gives similar results and its denoising results is independent to the selection of decomposition level; 2) generates stable statistical results; 3) can make use of mother wavelets with small filter size (i.e., low-order mother wavelets) that are suitable for preserving subtle features in vegetation spectrum; and 4) its denoising results do not depend on the selection of the mother wavelet when applying low-order mother wavelets.
Wavelet-based methods have been widely used for compression of remotely sensed images and data. Recently, second generation of wavelets which is based on a method called lifting has proven to be more effective than traditional wavelets as it provides lossless compression, lowers the memory usage, and is computationally faster. This study explores the literature related to applying second-generation wavelets for the compression of remote sensing data. Nevertheless, in order to compare the results of two wavelet types, some applications of traditional wavelets are also presented.
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