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With the growing importance of low-bandwidth applications, such as wireless access to the Internet, images are often sent or received at low bit rates. At these bit rates, they suffer from significant distortion and artifacts, making it difficult for those viewing the images to understand them. We present two progressive compression algorithms that focus on preserving the clarity of important image features, such as edges, at compression ratios of 80:1 and more. Both algorithms capture and encode the locations of important edges in the images. The first algorithm then transmits a standard SPIHT (set partitioning in hierarchical trees) bit stream, and at the decoder applies a nonlinear edge-enhancement procedure to improve the clarity of the encoded edges. The second approach uses a modified wavelet transform to "remove" the edges, and encodes the remaining texture information using SPIHT. With both approaches, features in the images that may be important for recognition are well preserved, even at low bit rates.