[Research] Implement spatial regularization for imaging

[KedoKudo]

Parent Epic

Part of #172 (2D Resonance Imaging)

Description

Implement spatial regularization to leverage neighboring pixel information.

Approach

Physical samples typically have:

• Spatial smoothness in composition
• Correlation between neighboring pixels
• Sharp boundaries at material interfaces

Use this prior knowledge to regularize fitting.

Methods to Consider

1. Spatial Binning (Simple)

• Aggregate N×N pixel blocks
• Trade spatial resolution for statistics

2. Gaussian Smoothing

• Apply Gaussian filter to initial estimates
• Use smoothed values as priors

3. Total Variation Regularization

• Penalize large gradients in abundance maps
• Preserves sharp edges
• Optimization-based approach

4. Graph-Based Regularization

• Model pixel relationships as graph
• Propagate information along edges

Proposed Interface

class SpatialRegularization:
    """Spatial regularization for 2D abundance fitting."""
    
    def __init__(
        self,
        method: str = "total_variation",  # or "gaussian", "graph"
        strength: float = 0.1,
    ):
        ...
    
    def regularize(
        self,
        initial_abundances: np.ndarray,  # (height, width)
        uncertainties: np.ndarray,
    ) -> np.ndarray:
        """Apply spatial regularization."""
        ...
    
    def iterative_fit(
        self,
        spectra: np.ndarray,  # (height, width, n_energies)
        n_iterations: int = 5,
    ) -> np.ndarray:
        """Iterative fitting with spatial regularization."""
        # Alternating: fit pixels → regularize → use as prior → refit
        ...

Tasks

• Implement simple spatial binning
• Implement Total Variation regularization
• Test on synthetic data with known spatial structure
• Compare methods on edge preservation
• Document trade-offs

Assignees

Jean (LANL)