Restoration Method of Hadamard Coding Spectral Imager.

Area of Science:

• Computational spectral imaging
• Optical engineering
• Signal processing

Background:

• Hadamard coding spectral imaging modulates and recovers spectral information using inverse transformation.
• Its multichannel detection advantage drives increasing research interest.
• Engineering realization faces challenges from push-broom error, template error, and detection noise.

Purpose of the Study:

• To present and analyze restoration methods for Hadamard coding spectral imaging instruments.
• To evaluate the robustness and suitability of different inverse solutions for engineering applications.
• To develop a real-time spectral reconstruction method and assess error impacts.

Main Methods:

• Comparison of three restoration methods: least squares, zero-filling inverse solution, and sparse method.
• Numerical and principle analysis of the Hadamard matrix's generalized orthogonality and its impact on solution stability.
• Development of a real-time spectral reconstruction algorithm based on the zero-filling inverse solution.

Main Results:

• The zero-filling inverse solution demonstrates superior robustness and stability due to direct use of the Hadamard matrix.
• Conditional number, error expectation, and covariance are more favorable with the zero-filling method.
• Simulation analysis indicates template noise and push error have a greater impact on reconstruction accuracy than detection error.

Conclusions:

• The zero-filling inverse solution is most suitable for engineering applications of Hadamard coding spectral imaging.
• Minimizing template noise and ensuring accurate push control are critical for reliable engineering realization.
• Reducing detection noise is also important, but secondary to controlling template and push errors.