Oscillation regularization

We measure the degree of oscillation of a sampled function f by the number of its local extrema. The greater this number, the more oscillatory and complex f becomes. In signal denoising, we want a restored function g that is simple and fits the data f well. We propose to model this by a global optimization, coined oscillation regularization, that reduces both the data fitting error and the number of local extrema of g: equation where err(f, g) measures the discrepancy between f and g and λ is a regularization parameter. To the best of our knowledge, the number of local extrema of g is a topological prior that is rarely exploited in the literature of regularization.