A Framework for Discrete Integral Transformations II—The 2D Discrete Radon Transform
SIAM Journal on Scientific Computing
Phase Aberration Correction of Ultrasonic Phased Array Signals
CISP '08 Proceedings of the 2008 Congress on Image and Signal Processing, Vol. 5 - Volume 05
An edge-guided image interpolation algorithm via directional filtering and data fusion
IEEE Transactions on Image Processing
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We develop a method to calculate 2D spectrum of a binary image with better quality than that obtained via direct 2D-FFT. With FFT, jagged edges of objects due to coarse sampling introduce artifacts into the frequency domain, especially in the high-frequency area. With the proposed method, Radon projections of the binary image along lines at different viewing angles are calculated. Each projection is extended by interpolation, then smoothed and decimated. The interpolation-smoothing-decimation operation is repeated several times to reduce ruggedness and improve quality of the Radon projections considerably. One-dimensional FFT of each refined Radon projection is calculated, resulting in a set of frequency-domain samples distributed on a polar coordinate system. These samples are interpolated onto a Cartesian grid to give the required 2D spectrum of the sampled binary image. Numerical computations on several objects show that the method can provide significant improvement to the spectrum as compared with direct 2D-FFT.