Locally monotonic regression is the optimal counterpart of iterated median filtering. In a previous paper, Restrepo and Bovik (see ibid., vol.41, no.9, p.2796-2810, 1993) developed an elegant mathematical framework in which they studied locally monotonic regressions in R/sup N/. The drawback is that the complexity of their algorithms is exponential in N. We consider digital locally monotonic regressions, in which the output symbols are drawn from a finite alphabet and, by making a connection to Viterbi decoding, provide a fast O(|A|/sup 2//spl alpha/N) algorithm that computes any such regression, where |A| is the size of the digital output alphabet, a stands for lomo degree, and N is the sample size. This is linear in N, and it renders the technique applicable in practice.
展开▼
机译：局部单调回归是迭代中值滤波的最佳对应。 Restrepo和Bovik（同上，第41卷，第9期，p.2796-2810，1993）在以前的论文中建立了一个优雅的数学框架，在其中他们研究了R / sup N /中的局部单调回归。缺点是它们的算法的复杂度在N中呈指数级。我们考虑数字局部单调回归，其中输出符号是从有限的字母中绘制的，并且通过与维特比解码连接，可以提供快速的O（| A | / sup 2 // spl alpha / N）算法，计算任何此类回归，其中| A |是数字输出字母的大小，a代表lomo度，N是样本大小。这在N中是线性的，这使该技术可在实践中应用。
展开▼
