Struct GraphSignalSmoother 

pub struct GraphSignalSmoother {
    pub alpha: f64,
}

Graph signal smoother via Tikhonov (graph Laplacian) regularization.

Solves the regularized least-squares problem:

minimize ‖x − y‖² + α xᵀ L x

where y is the observed (potentially noisy) signal, L is the graph Laplacian, and α > 0 is the regularization strength.

The closed-form solution is:

x* = (I + α L)⁻¹ y = U (I + α Λ)⁻¹ Uᵀ y

which can be computed efficiently using the GFT as a spectral filter with frequency response h(λ) = 1 / (1 + α λ).

Fields

alpha: f64

Regularization strength α > 0.

Implementations

impl GraphSignalSmoother

pub fn new(alpha: f64) -> Result<Self>

Create a smoother with regularization strength alpha.

pub fn smooth( &self, gft: &GraphFourierTransform, signal: &Array1<f64>, ) -> Result<Array1<f64>>

Smooth the observed signal y using the GFT basis.

Returns x* = U (I + α Λ)⁻¹ Uᵀ y.

pub fn frequency_response(&self, gft: &GraphFourierTransform) -> Array1<f64>

Return the frequency response function h(λ) = 1/(1 + α λ) evaluated at each graph frequency.

pub fn total_variation(adj: &Array2<f64>, signal: &Array1<f64>) -> Result<f64>

Compute the total variation (graph smoothness) of a signal: TV(x) = xᵀ L x = Σ_{(i,j)∈E} w_ij (x_i − x_j)².

Trait Implementations

impl Clone for GraphSignalSmoother

fn clone(&self) -> GraphSignalSmoother

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for GraphSignalSmoother

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.