In this paper we describe how the theory of wavelet thresholding introduced by Donoho and Johnstone can successfully be applied to two distinct problems in image processing where traditional linear filtering techniques are insufficient. The first application is related to speckle reduction in coherent imaging systems. We show that the proposed method works well for reducing speckle in SAR images while maintaining bright reflections for subsequent processing and detection. Secondly we apply the wavelet based method for reducing blocking artifacts associated with most DCT based image coders (e.g., most notably the Joint Photographic Experts Group (JPEG) standard at high compression ratios). In particular we demonstrate an algorithm for post-processing decoded images without the need for a novel coder/decoder. By applying this algorithm we are able to obtain perceptually superior images at high compression ratios using the JPEG coding standard. For both applications we have developed methods for estimating the required threshold parameter and we have applied these to large number of images to study the effect of the wavelet thresholding. Our main goal with this paper is to illustrate how the recent theory of wavelet denoising can be applied to a wide range of practical problems which does not necessarily satisfy all the assumptions of the developed theory.