This paper proposes an adaptive thresholding method for image denoising and compression using wavelet transforms. The threshold, called BayesShrink, is derived in a Bayesian framework based on the generalized Gaussian distribution (GGD) of wavelet coefficients. It is simple, closed-form, and adaptive to each subband, making it effective for image denoising. Experimental results show that BayesShrink performs well, often within 5% of the minimum mean squared error (MSE) of the best soft-thresholding benchmark. The paper also explores the use of lossy compression for denoising, where the zero-zone in the quantization step of compression is analogous to the threshold value in thresholding. The(coder) parameters are chosen based on Rissanen's minimum description length (MDL) principle. Experiments demonstrate that this method effectively reduces noise, especially for large noise levels, but introduces quantization noise. The paper concludes by discussing the potential for extending the method to other transform domains and future research directions.This paper proposes an adaptive thresholding method for image denoising and compression using wavelet transforms. The threshold, called BayesShrink, is derived in a Bayesian framework based on the generalized Gaussian distribution (GGD) of wavelet coefficients. It is simple, closed-form, and adaptive to each subband, making it effective for image denoising. Experimental results show that BayesShrink performs well, often within 5% of the minimum mean squared error (MSE) of the best soft-thresholding benchmark. The paper also explores the use of lossy compression for denoising, where the zero-zone in the quantization step of compression is analogous to the threshold value in thresholding. The(coder) parameters are chosen based on Rissanen's minimum description length (MDL) principle. Experiments demonstrate that this method effectively reduces noise, especially for large noise levels, but introduces quantization noise. The paper concludes by discussing the potential for extending the method to other transform domains and future research directions.