A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
Detection of Edges in Spectral Data II. Nonlinear Enhancement
SIAM Journal on Numerical Analysis
Reducing the Effects of Noise in Image Reconstruction
Journal of Scientific Computing
Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images
SIAM Journal on Numerical Analysis
Adaptive Edge Detectors for Piecewise Smooth Data Based on the minmod Limiter
Journal of Scientific Computing
Detection of Edges in Spectral Data III--Refinement of the Concentration Method
Journal of Scientific Computing
Recovery of Edges from Spectral Data with Noise—A New Perspective
SIAM Journal on Numerical Analysis
Iterative adaptive RBF methods for detection of edges in two-dimensional functions
Applied Numerical Mathematics
Edge detection from truncated Fourier data using spectral mollifiers
Advances in Computational Mathematics
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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.