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The decomposition of signals into their primitive or fundamental constituents play a vital role in removing noise or unwanted signals, thereby improving the quality and utility of the signals. There are various decomposition techniques, among which the linear wavelet technique and the Variational Mode Decomposition (VMD) are the most recent and widely used ones. This paper presents a comparative study of the decomposition of spatially inhomogeneous test functions namely Doppler and Bumps used by statisticians. An effort is made in this article to compare the efficiency of the noise removal in the resulting decompositions at various approximation levels using wavelets and by varying the number of reconstruction modes in VMD. Surprisingly it is found that the VMD technique yields better results with more accuracy for a specific set of parameters irrespective of the spatial character of the function.

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ABSTRACT:In this paper generic image watermarking technique is used for the copyright protection of color images. Watermarking with monochrome and translucent images based on One-to-One compound mapping of the values of the image pixels, which provide us the recovered image without any loss. Both the translucent full color and Opaque monochrome images are used in this paper. Two-fold monotonically increasing compound mapping is used to get more typical visible watermarks in the image. Measures have been taken to protect it from hackers.