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In this paper we consider two new techniques for image restoration, using order-constrained least-squares methods. The first technique consists of a cross-shaped moving window, within which two operations are combined. The first operation consists of simple hypothesis tests for monotonicity in both the horizontal and vertical directions. The second step finds the best least-squares fit of the input variates in both directions, constrained by the results of the hypothesis tests. The second technique consists of a square moving window, again combining two operations. With the first operation, we introduce a new edge detector with specific edge height δ. Based on detection or non-detection of an edge, we either apply order-constrained least-squares methods to determine the output, or simply average. The techniques described are applied to an actual noise-corrupted image.