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Image compression offers a good representation of images while using the least quantity of bits. Several lossy image coders are designed without considering the image nature. The image important information (e.g., edges) can be discarded at the coding quantization stage; that information is needed for image understanding and recognition. The possibility of saving storage space and preserving image important information in a joint way becomes imperative in areas such as medicine, mobile devices, and pattern recognition systems. This article addresses the design of an edge-preserving lossy image coder by means of wavelets and contourlets. The results obtained demonstrate the superior performance of the proposed coder against the traditional edge-preserving coders. The proposed coder ensures that the edges of an image are always preserved even at very low bit rates and the obtained decompressed images can be successfully used for future pattern recognition tasks.