Influence of sparse constraint functions on compressive holographic tomography

Area of Science:

• Computational imaging
• Digital holography
• Image reconstruction

Background:

• Compressive sensing is crucial for efficient holographic data acquisition.
• Sparse constraints, such as L1 and Total Variation (TV) norms, are vital for accurate reconstruction.
• Understanding their performance under varying conditions is essential for optimizing holographic tomography.

Purpose of the Study:

• To quantify and analyze the impact of L1 and TV norm sparse constraints on reconstruction quality.
• To investigate the influence of interlayer spacing, sampling rates, and signal-to-noise ratios.
• To provide guidance on selecting appropriate sparse constraints for compressive holographic tomography.

Main Methods:

• Comparative analysis of L1 and TV norm sparse constraints.
• Reconstruction quality evaluation under varied interlayer spacings, sampling rates, and signal-to-noise ratios.
• Theoretical explanation for interlayer spacing limitations.

Main Results:

• L1 norm yields higher reconstruction quality for high-quality holograms.
• TV norm provides stable and superior reconstruction for low-quality holograms.
• Interlayer spacing limitations were identified and explained.

Conclusions:

• The choice between L1 and TV norm depends on hologram quality.
• Recommends using the axial resolution of the digital holography system as the interlayer spacing.
• Findings aid in optimizing sparse constraint selection for compressive holographic tomography.