Indirect Hard Modeling (IHM) for Spectral Component Identification

This repository implements the Indirect Hard Modeling (IHM) method as described in the paper "Identification of Unknown Pure Component Spectra by Indirect Hard Modeling" by Kriesten et al., 2008. The code extracts pure spectra from a given spectral mixture matrix using a combination of peak fitting, correlation analysis, and optimization techniques.

---

Overview of the Method

The IHM approach models a spectral mixture matrix by:

1. Finding a representative spectrum (x_input) from a subset of mixture spectra (Step 1).
2. Fitting Voigt profiles to the peaks in x_input, capturing nonlinear effects like peak shifts and variations (Step 2).
3. Constructing a weight matrix representing contributions of the fitted peaks across all mixture spectra (Step 3).
4. Correlation-based analysis to identify distinctive and shared peaks, allowing classification of peaks into pure components (Step 4).
5. Delta matrix optimization to allocate shared peaks to their corresponding components, ensuring a coherent representation of the spectral data (Step 5).
6. Pure spectrum reconstruction using the optimized delta matrix to obtain individual pure spectra (Step 6).

---

Code Structure and Workflow

Step 1: Input Data

• Spectral Matrix: Provide your mixed spectral data in spectal_matrix. The matrix should have dimensions corresponding to the number of spectra and wavelength points.
• Wavelength Vector: Ensure wl matches the wavelength points of your spectral matrix.

Step 2: Finding x_input

• The code identifies a representative spectrum by averaging a subset of spectra with the lowest correlation errors.

Step 3: Voigt Peak Fitting

• Fits Voigt profiles to the representative spectrum (x_input) to extract peak parameters.
• Outputs:
  • Voigt Parameters: Saved to Voig_parameters_X_input.
  • Reconstructed Spectrum: Visualized alongside the mean spectrum.

Step 4: Weight Matrix Calculation

• Constructs the weight matrix W by fitting the Voigt parameters to all spectra in the dataset.
• Outputs:
  • Weight Matrix: Saved to WeightsMatrix.

Step 5: Correlation Analysis

• Constructs a peak-to-peak correlation matrix to classify peaks as:
  • Distinctive Peaks: Unique to individual components.
  • Shared Peaks: Common across multiple components.
• Determines the number of components (K) and identifies correlated groups of peaks.

Step 6: Delta Matrix Optimization

• Optimizes the delta matrix to allocate shared peaks to pure components using constrained optimization.

Step 7: Pure Spectrum Reconstruction

• Reconstructs the pure spectra using the optimized delta matrix.
• Outputs:
  • Reconstructed Spectra: Visualized alongside the original mean spectrum.

---

Usage Instructions

1. Prepare Input Data:

   • Replace spectal_matrix with your spectral data.
   • Provide the corresponding wavelength vector wl.

2. Run the Code:

   • Set run_fitting = True to perform new peak fitting. If previously run, set it to False to reuse saved results.
   • Set Only_SharedPeaks = True to optimize shared peaks only, if required.

---

References

• Kriesten, E., et al. (2008): "Identification of Unknown Pure Component Spectra by Indirect Hard Modeling".
  DOI:10.1016/j.chemolab.2008.05.002

---