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As successor to JPEG, JPEG2000 aims to realize a very low bitrate. Although JPEG2000's rate distortion has been improved by approximately 30% against JPEG, as on most images compressed using overlapping transforms-based algorithms, one can notice visible spurious oscillations, or ringing artifacts, around the edges of a JPEG2000-compressed image. In this paper, we propose a partial differential equations, or PDE-based image enhancement technique, in order to remove these ringing artifacts, while keeping the image's edges. Results are provided on grayscale and color images, showing a visible enhancement, confirmed by the PSNR increase.