| betathresh {gasper} | R Documentation |
Apply Beta Threshold to Data
Description
betathresh performs a generalized thresholding operation on the data y. The thresholding operation is parameterized by the parameter beta.
Usage
betathresh(y, t, beta = 2)
Arguments
y |
Numeric vector or matrix representing the noisy data. |
t |
Non-negative numeric value representing the threshold. |
beta |
Numeric value indicating the type of thresholding. |
Details
The function offers flexibility by allowing for different types of thresholding based on the beta parameter. Soft thresholding, commonly used in wavelet-based denoising corresponds to beta=1 . James-Stein thresholding corresponds to beta=2. The implementation includes a small constant for numerical stability when computing the thresholding operation.
The thresholding operator is defined as:
\tau(x,t) = x \max \left( 1 - t^{\beta} |x|^{-\beta}, 0 \right)
with \beta \geq 1.
Value
x Numeric vector or matrix of the filtered result.
References
Donoho, D. L., & Johnstone, I. M. (1995). Adapting to unknown smoothness via wavelet shrinkage. Journal of the american statistical association, 90(432), 1200-1224.
de Loynes, B., Navarro, F., & Olivier, B. (2021). Data-driven thresholding in denoising with spectral graph wavelet transform. Journal of Computational and Applied Mathematics, 389, 113319.
Examples
# Define a 2x2 matrix
mat <- matrix(c(2, -3, 1.5, -0.5), 2, 2)
# Apply soft thresholding with a threshold of 1
betathresh(mat, 1, 1)