Edge Detection of Piecewise Smooth Functions from UnderSampled Fourier Data Using Variance Signatures

DOI10.1137/16M1068013zbMath1365.65040MaRDI QIDQ5738168

Anne Gelb, Dennis Denker

Publication date: 31 May 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

algorithmvariancemagnetic resonance imagingimage reconstructionedge detectionFourier dataundersampling\(l^1\) regularization

Mathematics Subject Classification ID

Biomedical imaging and signal processing (92C55) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (2)

Fast iterative adaptive multi-quadric radial basis function method for edges detection of piecewise functions. I: Uniform mesh ⋮ Reducing effects of bad data using variance based joint sparsity recovery

Uses Software

• SAR image formation

Cites Work

• Nonlinear total variation based noise removal algorithms
• Image reconstruction from undersampled Fourier data using the polynomial annihilation transform
• Sparsity enforcing edge detection method for blurred and noisy Fourier data
• Hypothesis testing for Fourier based edge detection methods
• Edge detection from non-uniform Fourier data using the convolutional gridding algorithm
• Image reconstruction from Fourier data using sparsity of edges
• Detection of edges in spectral data
• Adaptive edge detectors for piecewise smooth data based on the minmod limiter
• The Split Bregman Method for L1-Regularized Problems
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• Improved Total Variation-Type Regularization Using Higher Order Edge Detectors
• Fundamentals of Radar Imaging
• Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
• Polynomial Fitting for Edge Detection in Irregularly Sampled Signals and Images

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