Regularized non-convex image reconstruction in digital holographic microscopy

Area of Science:

• Digital holography
• Image reconstruction
• Computational imaging

Background:

• Traditional spatial filtering methods in digital holography struggle with resolution recovery and introduce artifacts.
• Previous inverse problem approaches faced limitations in achieving strictly compatible solutions due to approximate intensity matching.

Purpose of the Study:

• To develop an advanced inverse problem method for digital holography image reconstruction.
• To improve resolution recovery and minimize artifacts compared to existing techniques.
• To achieve convergence to a strictly compatible solution in image reconstruction.

Main Methods:

• Replaced the non-convex image reconstruction problem with a sequence of surrogate convex problems.
• Designed an iterative numerical solver utilizing a data domain projection operator and Nesterov acceleration of the simultaneous Kaczmarz method.
• Employed multiresolution CDF 9/7 wavelet domain representation for regularization and energy-weighted preconditioning for minimum-norm solutions.

Main Results:

• Demonstrated superior resolution recovery in reconstructed images.
• Significantly reduced spurious artifacts in digital holography images.
• Showcased resilience to additive Gaussian noise and subsampling of intensity measurements.

Conclusions:

• The proposed inverse problem approach offers a robust and effective solution for digital holography image reconstruction.
• The method provides enhanced image quality with improved resolution and artifact reduction.
• The technique is adaptable to noisy and undersampled holographic data.