  Heavy sweep distortion induced by alignments and inter-reflections of layers
of a sample is a major burden in recovering 2D and 3D information in time
resolved spectral imaging. This problem cannot be addressed by conventional
denoising and signal processing techniques as it heavily depends on the physics
of the acquisition. Here we propose and implement an algorithmic framework
based on low-rank matrix recovery and alternating minimization that exploits
the forward model for THz acquisition. The method allows recovering the
original signal in spite of the presence of temporal-spatial distortions. We
address a blind-demodulation problem, where based on several observations of
the sample texture modulated by an undesired sweep pattern, the two classes of
signals are separated. The performance of the method is examined in both
synthetic and experimental data, and the successful reconstructions are
demonstrated. The proposed general scheme can be implemented to advance
inspection and imaging applications in THz and other time-resolved sensing
modalities.
