WhittakerSmoother

This MATLAB app smooths each row of a data matrix with the Whittaker method. It keeps the smoothed line close to the measured values while penalising rapid changes from one channel to the next. The value of lambda controls the balance: a small value follows the data more closely, while a large value produces a smoother line.

The method is written as:

minimize ||y - z||^2 + lambda ||D^2 z||^2

Rows are samples and columns are channels. The app shows the original and smoothed data and can export the result.

Start

addpath('path/to/WhittakerSmoother')
Whittaker_test
app = WhittakerSmoother(spectra);

The constructor accepts a numeric matrix or a struct. Struct data fields include data, spectra, matrix, and originalData. The optional x-axis may be supplied as wavelength, wavelengths, xAxis, x, or axis. If it is absent, channel numbers are used.

Input matrices must be nonempty, real, finite numeric 2-D arrays with at least three columns. The x-axis must have the same length as the matrix width and must increase or decrease without repeats.

Parameters and method

Parameter	Constraint
lambda	Finite positive number

The smoother always uses the second-difference penalty D^2; there is no selectable difference order. The calculation builds the corresponding system and solves it with a cached Cholesky factorization. The same factor is reused for all rows with the same channel count and lambda. A failed or non-finite solve is reported as an error.

The app previews one selected sample while parameters are edited. Lambda updates are throttled during slider movement, so the preview continues to change while the pointer is being dragged. The sample selector can be used to inspect different rows. The preview chart's + menu has an opt-in Show all spectra mode. It is off by default, loaded only on request, and refused above 500,000 plotted elements to avoid large browser/RAM transfers. After Apply, the result can be viewed as the mean, a sample of rows, or all rows. Display choices do not change the full result.

Result and calculation without the window

output = app.getData();

The output contains data, spectra, and smoothedData for the smoothed matrix, originalData, wavelength and wavelengths, the source name, the applied parameters, and metadata.

The calculation can also be used without the window:

addpath(fullfile('path/to/WhittakerSmoother', 'business_logic'))
core = WhittakerSmootherCore();
smoothed = core.smooth(spectra, 1e4);
[valid, message] = core.validateParams(1e4, size(spectra, 2));
stats = core.getCacheStats();

Changing the input or parameters makes the previous result out of date. Export is available only after a successful Apply with the current values.

Example data and tests

Whittaker_test.m creates noisy spectra with baseline drift:

Whittaker_test
app = WhittakerSmoother(spectra);

Run the checks from this folder:

runWhittakerSmootherTests
run_whittaker_assertions
run_whittaker_adversarial_tests

MATLAB R2022a or later is required. No additional toolbox is needed.

Reference

Eilers, P. H. C. (2003). A perfect smoother. Analytical Chemistry, 75(14), 3631-3636.

License: MIT