Cascade Coding With Error-Constrained Relative Entropy Decoding

This work develops iterative algorithms for decoding cascade-coded images by Relative Entropy (RE) minimization. In cascade coding, blocks ofanimage are firsttransform-coded and then theretained coefficients are transmitted by using moment-preserving Block Truncation Coding (BTC). The BTC coding introduces a quantization error in the values of the retained coefficients. Upon reception, the distorted coefficients are used in reconstructing the image by the inverse transform, with the unretained coefficients set equal to zero. The proposed algorithms reconstruct the original image from the distorted coefficients by minimizing the RE of the image, with the coefficients used as constraints. In addition, the error introduced by the BTC coding is used as an additional constraint, since it is known to the receiver by the nature of the BTC coding. The iterative nature of the algorithm pertains to the way the algorithm uses the constraints, i.e. one at a time, with each reconstruction used as a prior for the next RE minimization. This is the first time that RE minimization with errors in the constraints has been used in image decompression even though it is common in spectrum estimation when there are errors in the correlation measurements