WaveletThreshold operates on a DiscreteWaveletData object:

The result is a new DiscreteWaveletData object representing thresholded coefficients:

Specify thresholding method:

Use specific threshold function:

Also specify how to choose threshold value:

Inverse transform and compare:

Visualize the effect on wavelet coefficients:

Compare using WaveletListPlot:

Perform thresholding on specific wavelet indexes:

By default only the detail coefficients are thresholded:

Use Automatic to threshold coefficients used in the inverse transform:

Use All to threshold all coefficients:

Use {wind₁,wind₂,…} to fully control which coefficients to threshold:

Compare the resulting coefficients:

Smooth noisy data using automatic thresholding methods:

Compare all named automatic thresholding methods tspec:

Choose specific thresholding function tfun to apply:

Reconstruct data from thresholded coefficients with automatically chosen threshold value:

Use a named method to automatically compute the threshold value :

Reconstruct data after "Soft" thresholding with various threshold value selection methods:

Use a specific numerical threshold value :

The best smoothing occurs for threshold values that are similar to the scale of the noise:

Use a function to compute a threshold value :

Threshold all coefficients below the standard deviation:

Plot the effect of thresholding function tfun on coefficient values ranging from -0.5 to 0.5:

Apply thresholding separately at each refinement level to data varying on different scales:

Different methods for selecting separate threshold values at each level:

Compare with methods that choose one threshold value for all levels:

Perform thesholding by specifying a function and wavelet index to compute :

Threshold all detail coefficients below the standard deviation:

Data processing pipeline for simple automatic smoothing:

Denoise 1D data:

Denoise 2D data:

Add normally distributed noise with standard deviation σ:

Compare effectiveness of automatic smoothing for different noise levels:

Threshold specific components of an image:

Strongly threshold horizontal and vertical detail coefficients {___,1|2} only:

Compare coefficients:

The inverse transform image has mainly diagonal features:

Plot the noise subtracted by different thresholding functions tfun with automatic threshold value:

Subtract smoothed data from original data (giving a noise model):

Compare performance of automatic thresholding methods when smoothing noisy data:

Quantify performance using SNR (signal-to-noise ratio) and peak SNR in decibels (dB):

Smooth by applying thresholding method th to detail coefficients {___,1}:

Compare all named automatic thresholding methods; higher value is better:

Plot smoothed data together with perfectly noise-free data:

"Universal" thresholding value:

Perform a LiftingWaveletTransform:

The mean absolute deviation is computed using detail coefficients at first refinement level {1}:

Compute universal threshold value as and perform a "Hard" threshold:

Use WaveletThreshold to compute the "Universal" threshold value:

Compare threshold values:

"SURE" thresholding value:

Perform a LiftingWaveletTransform:

Compute "SURE" threshold values :

Use WaveletThreshold to compute "SURE" threshold value:

Compare threshold values:

"FDR" thresholding value:

Perform a LiftingWaveletTransform:

Estimate noise level:

For each wavelet coefficient , find its two-sided -value :

Order the according to their size . Find , where is the significance level:

Compute threshold as :

Use WaveletThreshold to compute "FDR" threshold value:

Compare threshold values: