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The conventional two-dimensional wavelet transform used in existing image coders is usually performed through one-dimensional (1-D) filtering in the vertical and horizontal directions, which cannot efficiently represent edges and lines in images. The curved wavelet transform presented in this paper is carried out by applying 1-D filters along curves, rather than being restricted to vertical and horizontal straight lines. The curves are determined based on image content and are usually parallel to edges and lines in the image to be coded. The pixels along these curves can be well represented by a small number of wavelet coefficients. The curved wavelet transform is used to construct a new image coder. The code-stream syntax of the new coder is the same as that of JPEG2000, except that a new marker segment is added to the tile headers. Results of image coding and subjective quality assessment show that the new image coder performs better than, or as well as, JPEG2000. It is particularly efficient for images that contain sharp edges and can provide a PSNR gain of up to 1.67 dB for natural images compared with JPEG2000.