TAILIEUCHUNG - The Essential Guide to Image Processing- P17

The Essential Guide to Image Processing- P17:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | 488 CHAPTER 18 Wavelet Image Compression FIGURE Tling representations of several expansions for 1D signals. a STFT-like decomposition b wavelet decomposition c wavelet packet decomposition and d anti-wavelet packet decomposition. Fig. d highlights a wavelet packet expansion where the time-frequency attributes are exactly the reverse of the wavelet case the expansion has good frequency resolution at higher frequencies and good time localization at lower frequencies we might call this the anti-wavelet packet. There are a plethora of other options for the time-frequency resolution tradeoff and these all correspond to admissible wavelet packet choices. The extra adaptivity of the wavelet packet framework is obtained at the price of added computation in searching for the best wavelet packet basis so an efficient fast search algorithm is the key in applications involving wavelet packets. The problem of searching for the best basis from the wavelet packet library for the compression problem using an RD optimization framework and a fast tree-pruning algorithm was described in 22 . The 1D wavelet packet bases can be easily extended to 2D by writing a 2D basis function as the product of two 1D basis functions. In another words we can treat the rows and columns of an image separately as 1D signals. The performance gains associated with wavelet packets are obviously image-dependent. For difficult images such as Barbara in Fig. a wavelet packet decomposition shown in Fig. a gives much better coding performance than the wavelet decomposition. The wavelet packet decoded Barbara image at b p is shown in Fig. b whose visual quality or PSNR is the same as the wavelet SPIHT decoded Barbara image at b p in Fig. . The bit rate saving achieved by using a wavelet packet basis instead of the wavelet basis in this case is 27 at the same visual quality. An important practical application of wavelet packet expansions is the FBI wavelet scalar .

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