Method of optimal out-of-band correction for multispectral remote sensing

The method comprising:

• providing training hyperspectral data and at least one optical filter,
• simulating expected band-averaged spectral radiances image vector from the training hyperspectral data and at least one filter transmittance function corresponding to the at least one optical filter;
• simulating measured band-averaged spectral radiances image vector from the training hyperspectral data and the at least one transmittance function;
• providing a cost function comprising total errors between the simulated expected band-averaged spectral radiances image vector and the simulated measured band-averaged spectral radiances image vector, and an out-of-band transform matrix parameter;
• optimizing the cost function by applying a least-squares best fit to the cost function using the out-of-band transform matrix parameter to generate a linear out-of-band correction transform;
• calculating a cross-correlation matrix of an expected band-averaged spectral radiances image vector and the realistic measured band-averaged spectral radiances image vector;
• calculating an auto-correlation matrix of the realistic measured band-averaged spectral radiances image vector;
• generating an optimal out-of-band transform matrix by matrix-multiplying the cross-correlation matrix and an inverse of the auto-correlation matrix;
• providing a realistic measured band-averaged spectral radiances image vector from the at least one optical filter;
• and
• generating a realistic recovered band-averaged spectral radiances image vector by matrix-multiplying the optimal out-of-band transform matrix and the realistic measured band-averaged spectral radiances image vector, the realistic recovered band-averaged spectral radiances image vector being free of out-of-band effects.