Spectral representation of principal components in signals and images using G-lets decomposition of subbands

This paper presents a spectral subband decomposition using G-lets in time-domain for 1-D and 2-D signals. The decomposition is achieved through successive filtering and decimation steps ending up in a decomposition tree. At each node of the tree, the parameters of the corresponding subband signal are estimated using high gradients obtained at the first node. The resulting subbands are found to highlight the components of the signal. The proposed method using G-lets enables one to reduce the processing time and makes the choice of decomposition levels easier, comparatively to the case where the whole signal is processed at once. The advantage of G-lets based subbands is demonstrated using 1-D and 2-D signals. It is seen that a synthetic signal generated from a sine and cosine signal is separated into exactly the same two signals and the performance is good for monocomponent and multicomponent signals.