Hypothesis testing for fourier based edge detection methods

Edge detection is an essential task in image processing. In some applications, such as Magnetic Resonance Imaging, the information about an image is available only through its frequency (Fourier) data. In this case, edge detection is particularly challenging, as it requires extracting local information from global data. The problem is exacerbated when the data are noisy. This paper proposes a new edge detection algorithm which combines the concentration edge detection method (Gelb and Tadmor in Appl. Comput. Harmon. Anal. 7:101-135, 1999) with statistical hypothesis testing. The result is a method that achieves a high probability of detection while maintaining a low probability of false detection.