Band-Stop Smoothing Filter Design

Smoothness priors and quadratic variation (QV) regularization are widely used techniques in many applications ranging from signal and image processing, computer vision, pattern recognition, and many other fields of engineering and science. In this contribution, an extension of such algorithms to band-stop smoothing filters (BSSFs) is investigated. For designing a BSSF, the most important parameters are the order and the cutoff frequencies. In this paper, we show that with the optimization approaches (smoothness priors or QV regularization), the cutoff frequencies are related to the regularized parameters and the order can be directly (and easily) controlled with the number of derivatives. We describe two ways to implement the BSSFs using these approaches. First, we present a parallel structure to BSSF and then illustrate why it is less than ideal. Next, we present a novel approach regarding parallel structure to produce BSSFs with very sharp transition bands for high-performance applications. An improved optimization-based approach to BSSF design is introduced. The performance of the new BSSFs is nearly ideal.