Speckle reduction in digital holography by fast adaptive three-operator splitting low-rank total variation filtering

In the field of digital holography, speckle noise severely degrades the quality of reconstructed images. We propose an adaptive three-operator splitting low-rank total variation (ATOS-LRTV) method to fast and efficiently suppress the speckle noise in the reconstructed image of the digital hologram. The three-operator splitting (TOS) algorithm is integrated into low-rank total variation (LRTV) with an adaptive parameter adjustment mechanism in the proposed framework to effectively resolve the conflict between denoising performance and computational efficiency. The synchronous update scheme of TOS replaces the alternating direction multiplier method in conventional LRTV to disassemble complex optimization problems into parallelizable sub-problems, whereas the adaptive mechanism dynamically adjusts the regularization parameters to improve the reconstruction accuracy. The experimental results demonstrate that the proposed method effectively suppresses speckle at the fast speeds and achieves an average peak signal-to-noise ratio of 35 dB and a Structural Similarity Index Measure of 0.95. The ATOS-LRTV method can be applied to such fields as 3D display, industrial testing, and medical diagnosis.