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A new secret writing using DES and DEFLATE algorithm is explored by improving the previous attempts in this sense in terms of security and compression. A Matching Pursuit algorithm using redundant basis decomposition technique is used to securely hide a message. The stability and computational complexity problems are solved by introducing new selection and update rules working entirely in the integer domain. Image decomposition is randomized in several ways thus improving the stego-message undetectability, and making the hidden message undetectable by targeted steganalyzers. A refinement decomposition step is applied to the three color bands to increase the stego-message payload.
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