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We develop an iterative, hillclimbing-based assignment algorithm for the approximate solution of discrete-parameter cost minimization problems defined on the pixel sites of an image. While the method is applicable to a number of problems including encoding, decoding, and segmentation, this article focuses on entropy-constrained encoding. For typical statistical image models, the globally optimal solution requires an intractable exhaustive search, while standard greedy methods, though tractable in computation, may be quite suboptimal. Alternatively, our method is guaranteed to perform no worse (and typically performs significantly better) than greedy encoding, yet with manageable increases in complexity. The new approach uses dynamic programming as a local optimization "step," repeatedly applied to the rows (or columns) of the image, until convergence. For a DCT framework, with entropy-constrained TCQ applied to the coefficient sources, the new method gains as much as 0.8 dB over standard greedy encoding.