Robust Kramers–Kronig holographic imaging with Hilbert–Huang transform

Holography based on Kramers-Kronig relations (KKR) is a promising technique due to its high-space-bandwidth product. However, the absence of an iterative process limits its noise robustness, primarily stemming from the lack of a regularization constraint. This Letter reports a generalized framework aimed at enhancing the noise robustness of KKR holography. Our proposal involves employing the Hilbert-Huang transform to connect the real and imaginary parts of an analytic function. The real part is initially processed by bidimensional empirical mode decomposition into a series of intrinsic mode functions (IMFs) and a residual term. They are then selected to remove the noise and bias terms. Finally, the imaginary part can be obtained using the Hilbert transform. In this way, we efficiently suppress the noise in the synthetic complex function, facilitating high-fidelity wavefront reconstruction using ∼20% of the exposure time required by existing methods. Our work is expected to expand the applications of KKR holography, particularly in low phototoxicity biological imaging and other related scenarios.