Establish convergence and physical validity of spectral image restoration

Establish whether the pseudo Lucy–Richardson spectral image restoration algorithm based on the contribution matrix \(\mathbf{A}_j\) converges and produces a physically meaningful solution for restored solar spectral scans.

Background

The spectral restoration procedure reconstructs solar spectral scans using a contribution matrix that accounts for the time-dependent point-spread-function contributions from adjacent frames. Unlike ordinary two-dimensional convolution, this operator is generally neither uniform nor symmetric, so standard convergence results for Lucy–Richardson deconvolution do not directly apply.

The thesis reports that the algorithm converged to meaningful solutions in the cases tested, but explicitly notes that a mathematical justification is absent. Establishing convergence and physical validity would provide a theoretical foundation for the restoration method.