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A method for the lossy compression of multivalued images using transform-based Boolean minimization is described. Blocks in bit-planes of an image are minimized, and the results of these minimizations are used to detect and reduce noise (sandy regions) and spatial complexity in the blocks. Specifically, the techniques of "minterm uniformalization" and "minterm quantization and thresholding" are presented as methods of discarding perceptually insignificant information from a minimized representation of an image and use data readily available from minimization without the calculation of complicated measures. Experimentally, results comparable to JPEG and better than existing binary techniques can be expected. Fast algorithms may be used, no multiplications are required, and decompression is performed without an inverse transform. Therefore, an emphasis is placed on the use of these algorithms for low-complexity or very high-speed hardware implementations for communications, for distributed and parallel sensor and computing applications, as well as for database storage.