A test for the absence of aliasing or white noise in two-dimensional locally stationary wavelet processes

Abstract

Either intentionally or unintentionally, sub-sampling is a common occurrence in image processing and can lead to aliasing if the highest frequency in the underlying process is higher than the Nyquist frequency. Several techniques have already been suggest in order to prevent aliasing from occurring (for example applying anti-aliasing filters), however there is little work describing methods to detect for it. Recently, Eckley and Nason (Biometrika 105(4), 833–848, 2018) developed a test for the absence of aliasing and/or white noise in locally stationary wavelet processes. Following Eckley and Nason (Biometrika 105(4), 833–848, 2018), we derive the corresponding theoretical consequences of sub-sampling a two-dimensional locally stationary wavelet process and develop a procedure to test for the absence of aliasing and/or white noise confounding at a fixed point, demonstrating its effectiveness and use through appropriate simulation studies and an example. In addition, we outline some possibilities for extending these methods further, from images to videos.