2019/07/02 by Amir Averbuch, Averbuch, Amir, Pekka Neittaanmäki +5 · 1 citation
Agricultural and Biological Sciences · Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Scientific Research Methods #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA) #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1907.01479
openalex publication_date 2019/07/02 · arxiv created 2019/07/03 · arxiv updated 2019/07/04 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based orthonormal WPs designed in [2]. The imaginary parts are the so-called complementary orthonormal WPs, which, unlike the symmetric regular WPs, they are antisymmetric. Tensor products of 1D quasi-analytic WPs provide a diversity of 2D WPs oriented in multiple directions. For example, a set of the fourth-level WPs comprises 62 different directions. The designed computational scheme in the paper enables us to get fast and easy implementation of the WP transforms. The presented WPs proved to be efficient in signal/image processing applications such as restoration of images degraded by either additive noise or missing of up to 90% of their pixels.