Wavelet Denoising

step_measure_smooth_wavelet() creates a specification of a recipe step that applies wavelet-based denoising to measurement data. This method is particularly effective for signals with localized features like peaks.

Usage

step_measure_smooth_wavelet(
  recipe,
  measures = NULL,
  wavelet = "DaubExPhase",
  filter_number = 4L,
  threshold_type = c("soft", "hard"),
  threshold_policy = c("universal", "sure", "cv"),
  levels = NULL,
  role = NA,
  trained = FALSE,
  skip = FALSE,
  id = recipes::rand_id("measure_smooth_wavelet")
)

Arguments

recipe

A recipe object.

measures

An optional character vector of measure column names.

wavelet

The wavelet family to use. Default is "DaubExPhase". Options include "DaubExPhase", "DaubLeAsworthy", "Lawton".

filter_number

The filter number within the wavelet family. Default is 4. Higher numbers give smoother wavelets.

threshold_type

Type of thresholding: "soft" (default) or "hard". Soft thresholding shrinks coefficients toward zero; hard thresholding sets small coefficients exactly to zero.

threshold_policy

How to determine the threshold:

• "universal" (default): Uses universal threshold sqrt(2*log(n))

• "sure": Stein's Unbiased Risk Estimate

• "cv": Cross-validation

levels

Number of decomposition levels. Default is NULL (auto).

role

Not used.

trained

Logical indicating if the step has been trained.

skip

Logical. Should the step be skipped when baking?

id

Unique step identifier.

Value

An updated recipe with the new step added.

Details

Wavelet denoising works by:

1. Decomposing the signal into wavelet coefficients

2. Thresholding small coefficients (presumed to be noise)

3. Reconstructing the signal from remaining coefficients

This approach is powerful because:

• It adapts to local signal characteristics

• It preserves sharp features like peaks

• It can separate noise from signal at multiple scales

Requires the wavethresh package to be installed.

Note

Wavelet transforms require signal lengths that are powers of 2. Signals are automatically padded to the next power of 2 and trimmed after processing.

See also

Other measure-smoothing: step_measure_despike(), step_measure_filter_fourier(), step_measure_savitzky_golay(), step_measure_smooth_gaussian(), step_measure_smooth_ma(), step_measure_smooth_median()

Examples

library(recipes)

rec <- recipe(water + fat + protein ~ ., data = meats_long) |>
  update_role(id, new_role = "id") |>
  step_measure_input_long(transmittance, location = vars(channel)) |>
  step_measure_smooth_wavelet() |>
  prep()

bake(rec, new_data = NULL)
#> # A tibble: 215 × 5
#>       id water   fat protein .measures
#>    <int> <dbl> <dbl>   <dbl>    <meas>
#>  1     1  60.5  22.5    16.7 [100 × 2]
#>  2     2  46    40.1    13.5 [100 × 2]
#>  3     3  71     8.4    20.5 [100 × 2]
#>  4     4  72.8   5.9    20.7 [100 × 2]
#>  5     5  58.3  25.5    15.5 [100 × 2]
#>  6     6  44    42.7    13.7 [100 × 2]
#>  7     7  44    42.7    13.7 [100 × 2]
#>  8     8  69.3  10.6    19.3 [100 × 2]
#>  9     9  61.4  19.9    17.7 [100 × 2]
#> 10    10  61.4  19.9    17.7 [100 × 2]
#> # ℹ 205 more rows