fmri_wiener
===========

.. currentmodule:: fmri_toolbox

Description
-----------
FMRI_WIENER  Wiener deconvolution: estimate neural signal from BOLD response.
Estimates the underlying neural activity time series from an observed BOLD
signal using Wiener deconvolution. The method works in the frequency domain:
it divides the BOLD spectrum by the HRF spectrum while applying a regulariser
(the noise term) to suppress amplification of noise at frequencies where the
HRF has low power.

Usage
-----
.. code-block:: matlab

    neural = fmri_wiener(bold, hrf, noise_level)

Inputs
------
- **BOLD**: Observed BOLD time series (N x 1). Will be mean-centred.
- **HRF**: Haemodynamic response function sampled at the same rate as BOLD (M x 1). Does not need to be the same length as BOLD; it will be zero-padded to match. A canonical HRF can be generated with fmri_doublegamma.
- **NOISE_LEVEL**: Regularisation strength: noise power relative to BOLD amplitude. Typical range: 0.05 to 0.20. Default: 0.1

Outputs
-------
- **NEURAL**: Estimated neural time series (N x 1), same length as BOLD.

Examples
--------
.. code-block:: matlab

    % Generate canonical HRF at TR = 2s
    t   = 0:2:32;
    hrf = fmri_doublegamma(t);
    % Deconvolve BOLD signal from one voxel
    bold_ts = data(voxel_idx, :)';
    neural  = fmri_wiener(bold_ts, hrf', 0.1);

Notes
-----
- Results are sensitive to the noise_level parameter. Too low: noisy output.
- Too high: over-smoothed, response is blurred. Values of 0.05-0.20 are
- typically reasonable for standard fMRI data.

References
----------
- Wiener, N. (1949). Extrapolation, Interpolation, and Smoothing of Stationary Time Series. MIT Press.

See Also
--------
- fmri_doublegamma
- fmri_corregressor
- fmri_detrend