Abstract-The method of wavelet thresholding for removing noise, or denoising, has been researched extensively due to its effectiveness and simplicity. Much of the literature has focused on developing the best uniform threshold or best basis selection. However, not much has been done to make the threshold values adaptive to the spatially changing statistics of images. Such adaptivity can improve the wavelet thresholding performance because it allows additional local information of the image (such as the identification of smooth or edge regions) to be incorporated into the algorithm. This work proposes a spatially adaptive wavelet thresholding method based on context modeling, a common technique used in image compression to adapt the coder to changing image characteristics. Each wavelet coefficient is modeled as a random variable of a generalized Gaussian distribution with an unknown parameter. Context modeling is used to estimate the parameter for each coefficient, which is then used to adapt the thresholding strategy. This spatially adaptive thresholding is extended to the overcomplete wavelet expansion, which yields better results than the orthogonal transform. Experimental results show that spatially adaptive wavelet thresholding yields significantly superior image quality and lower MSE than the best uniform thresholding with the original image assumed known.

Undecaprenyl pyrophosphate synthase (UPPs) catalyzes chain elongation of farnesyl pyrophosphate (FPP) to undecaprenyl pyrophosphate (UPP) via condensation with eight isopentenyl pyrophosphates (IPP). UPPs from Escherichia coli is a dimer, and each subunit consists of 253 amino acid residues. The chain length of the product is modulated by a hydrophobic active site tunnel. In this paper, the crystal structure of E. coli UPPs was refined to 1.73 Å resolution, which showed bound sulfate and magnesium ions as well as Triton X-100 molecules. The amino acid residues 72-82, which encompass an essential catalytic loop not seen in the previous apoenzyme structure (Ko, T. Undecaprenyl pyrophosphate synthase (UPPs) 1 catalyzes the consecutive condensation reactions of eight molecules of isopentenyl pyrophosphate (IPP) with farnesyl pyrophosphate (FPP) to form a lipid carrier to mediate bacterial peptidoglycan synthesis (1-3). This enzyme belongs to a family of prenyltransferases that make linear IPP condensation products with designate chain lengths (4). These enzymes are divided into trans-type and cis-type, which catalyze the trans-and cisdouble bond formation during each IPP condensation, respectively (5, 6). Unlike trans-prenyltransferases, which tend to make short and medium chain-length products ranging from C 15 to C 50 , UPPs and other cis-prenyltransferases mostly generate ՆC 55 long-chain products. Significant sequence homology has been found within the cis-and trans-prenyltransferases, but the two groups of enzymes do not share sequence similarity (7,8). Among the trans-prenyltransferases, the crystal structure of avian farnesyl pyrophosphate synthase has been solved almost a decade ago, and the mechanism has been elucidated (9). However, only recently have the first crystal structures of cis-prenyltransferase (UPPs) become available (10, 11), and they provide a template for modeling other cis-enzymes such as dehydrodolichyl pyrophosphate synthase from yeast and human and a polyprenyl pyrophosphate synthase discovered in Arabidopsis thaliana (12,13).UPPs from Escherichia coli is a dimer of identical subunits of 253 amino acids. The three-dimensional structure of the apoenzyme reveals an elongated tunnel-shaped active site crevice surrounded by two ␣-helices and four ␤-strands (11). Previous site-directed mutagenesis studies suggested that the substrates FPP and IPP are bound on top of the tunnel, and the farnesyl moiety of FPP migrates toward its bottom during product chain elongation (14 -16). The tunnel is sealed at the bottom by the side chain of . In the crystal structure of UPPs from Micrococcus luteus, a sulfate ion bound to a conserved structural P-loop represents the location of the pyrophosphate moiety of FPP (10).The previous E. coli UPPs crystal was grown using polyethylene glycol (PEG), and no sulfate ion was observed (11). Metal ion was not found in both apo-UPPs structures, although the enzyme requires Mg 2ϩ for activity. Two protein conformers of the E. coli UPPs were observed, i.e. one with a bou...

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