This paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, using the generalized Gaussian distribution (GGD) as the prior for wavelet coefficients. The proposed threshold, called BayesShrink, is simple and closed-form, and it is adaptive to each subband based on data-driven estimates of the parameters. Experimental results show that BayesShrink performs well, typically within 5% of the MSE of the best soft-thresholding benchmark. It also outperforms SureShrink most of the time. The paper also explores the use of lossy compression for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed for denoising, achieving simultaneous denoising and compression. The zero-zone in the quantization step is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on the minimum description length (MDL) principle. Experiments show that this compression method effectively removes noise, especially for large noise power, though it introduces quantization noise. The paper discusses wavelet thresholding for image denoising and compression. The soft-thresholding method is chosen over hard-thresholding due to its near-optimal performance and better visual results. The proposed Bayesian risk minimization is subband-dependent, and the threshold is found to be $ T_B = \sigma^2 / \sigma_X $, where $ \sigma^2 $ is the noise variance and $ \sigma_X $ is the signal variance. This threshold is data-driven, with parameters estimated from the observed data. The paper also discusses the MDL principle for compression-based denoising. The MDLQ criterion is used to determine the quantization parameters, balancing the trade-off between compression rate and distortion. The results show that BayesShrink performs well, with MSE within 5% of OracleShrink for smoother images and up to 8% better than SureShrink for detailed images. The MDLQ-based compression introduces quantization noise but achieves significant noise reduction for larger noise levels. The results demonstrate that compression can achieve denoising, especially for larger noise levels.This paper proposes an adaptive, data-driven threshold for image denoising via wavelet soft-thresholding. The threshold is derived in a Bayesian framework, using the generalized Gaussian distribution (GGD) as the prior for wavelet coefficients. The proposed threshold, called BayesShrink, is simple and closed-form, and it is adaptive to each subband based on data-driven estimates of the parameters. Experimental results show that BayesShrink performs well, typically within 5% of the MSE of the best soft-thresholding benchmark. It also outperforms SureShrink most of the time. The paper also explores the use of lossy compression for denoising. The BayesShrink threshold can aid in the parameter selection of a coder designed for denoising, achieving simultaneous denoising and compression. The zero-zone in the quantization step is analogous to the threshold value in the thresholding function. The remaining coder design parameters are chosen based on the minimum description length (MDL) principle. Experiments show that this compression method effectively removes noise, especially for large noise power, though it introduces quantization noise. The paper discusses wavelet thresholding for image denoising and compression. The soft-thresholding method is chosen over hard-thresholding due to its near-optimal performance and better visual results. The proposed Bayesian risk minimization is subband-dependent, and the threshold is found to be $ T_B = \sigma^2 / \sigma_X $, where $ \sigma^2 $ is the noise variance and $ \sigma_X $ is the signal variance. This threshold is data-driven, with parameters estimated from the observed data. The paper also discusses the MDL principle for compression-based denoising. The MDLQ criterion is used to determine the quantization parameters, balancing the trade-off between compression rate and distortion. The results show that BayesShrink performs well, with MSE within 5% of OracleShrink for smoother images and up to 8% better than SureShrink for detailed images. The MDLQ-based compression introduces quantization noise but achieves significant noise reduction for larger noise levels. The results demonstrate that compression can achieve denoising, especially for larger noise levels.