Sparsity Enforcing Edge Detection Method for Blurred and Noisy Fourier data
Journal of Scientific Computing
Hypothesis Testing for Fourier Based Edge Detection Methods
Journal of Scientific Computing
Iterative Design of Concentration Factors for Jump Detection
Journal of Scientific Computing
Edge detection from truncated Fourier data using spectral mollifiers
Advances in Computational Mathematics
Multi-metric learning for multi-sensor fusion based classification
Information Fusion
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We consider the problem of detecting edges—jump discontinuities in piecewise smooth functions from their $N$-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the “smoothness" scale of order $1/N$, the noise scale of order $\sqrt{\eta}$, and the $\mathcal{O}(1)$ scale of the jump discontinuities. We use concentration factors which are adjusted to the standard deviation of the noise $\sqrt{\eta} \gg 1/N$ in order to detect the underlying $\mathcal{O}(1)$-edges, which are separated from the noise scale $\sqrt{\eta} \ll 1$.