Abstract-The first part of this paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, and the prior used on the wavelet coefficients is the generalized Gaussian distribution (GGD) widely used in image processing applications. The proposed threshold is simple and closed-form, and it is adaptive to each subband because it depends on data-driven estimates of the parameters. Experimental results show that the proposed method, called BayesShrink, is typically within 5% of the MSE of the best soft-thresholding benchmark with the image assumed known. It also outperforms Donoho and Johnstone's SureShrink most of the time.The second part of the paper attempts to further validate recent claims that lossy compression can be used for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed with the intention of denoising, and thus achieving simultaneous denoising and compression. Specifically, the zero-zone in the quantization step of compression is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on a criterion derived from Rissanen's minimum description length (MDL) principle. Experiments show that this compression method does indeed remove noise significantly, especially for large noise power. However, it introduces quantization noise and should be used only if bitrate were an additional concern to denoising.Index Terms-Adaptive method, image compression, image denoising, image restoration, wavelet thresholding.

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The reaction of nitrogen dioxide with aqueous sulfite solutions, in the presence and in the absence of oxygen, has been studied using Raman spectroscopy to determine product concentrations. The products observed include nitrite, sulfate, and dithionate ions. The reaction appears to initially produce nitrite ion and sulfite radical: NO2 + S032" -* NO2-+ SO3•-. The sulfite radical can undergo either recombination or reaction with oxygen to form SO5•-. In the absence of oxygen, we obtain a ratio of [S042-]/[S2C>62-] = 1.8 ± 0.3, reflecting the branching of the recombination of sulfite radical: SO3-+ SO3•--* S2O62-or SO3•-+ S03--*• SO32-+ SO3. The production of S03-and SO5•-radicals from the nitrogen dioxidesulfite ion reaction suggests that this reaction could contribute significantly to S(IV) oxidation in atmospheric aerosols under suitable conditions.