Enhancing Digital Hologram Reconstruction Using Reverse-Attention Loss for Untrained Physics-Driven Deep Learning Models with Uncertain Distance

TL;DR

This work proposes reverse-attention loss, a weighted sum of losses for all possible candidates with learnable weights that presents a significant reconstruction performance over rival methods and even is almost equal to that achieved with a precisely known object distance.

Abstract

Untrained Physics-based Deep Learning (DL) methods for digital holography have gained significant attention due to their benefits, such as not requiring an annotated training dataset, and providing interpretability since utilizing the governing laws of hologram formation. However, they are sensitive to the hard-to-obtain precise object distance from the imaging plane, posing the $\textit{Autofocusing}$ challenge. Conventional solutions involve reconstructing image stacks for different potential distances and applying focus metrics to select the best results, which apparently is computationally inefficient. In contrast, recently developed DL-based methods treat it as a supervised task, which again needs annotated data and lacks generalizability. To address this issue, we propose $\textit{reverse-attention loss}$, a weighted sum of losses for all possible candidates with learnable weights. This is a pioneering approach to addressing the Autofocusing challenge in untrained deep-learning methods. Both theoretical analysis and experiments demonstrate its superiority in efficiency and accuracy. Interestingly, our method presents a significant reconstruction performance over rival methods (i.e. alternating descent-like optimization, non-weighted loss integration, and random distance assignment) and even is almost equal to that achieved with a precisely known object distance. For example, the difference is less than 1dB in PSNR and 0.002 in SSIM for the target sample in our experiment.

Figures (5)

• Figure 1: Comparison of the untrained DL-based method for different scenarios: (a) the precise object distance is known, (b) the precise object distance is unknown and using conventional Autofocusing methods, and (c) the precise object distance is unknown and using our proposed method. The sample is from P1170.
• Figure 2: The example of reconstruction by DeepDIH using different object distances. The actual distance is $5000\mu m$.
• Figure 3: The computational graph of the model $\Theta$ with the proposed loss. (a) Forward-propagation; (b) Backward-propagation. The red arrows denote the gradient of these weights, which will be detached in the backward-propagation. Note this propagation is for updating the neural network, which is different from the propagation of optical waves.
• Figure 4: The synthetic noisy quadratic analysis of convergence for $n= 2, 5,20,100$. First Row: The error surface of candidate losses (gray), the ground loss (red) (i.e. with the precise distance), and reverse-attention loss (blue). The dot point presents the update step with a known object distance (red) or without a known object distance (blue). First Row: The convergence rate of the ground loss and reverse-attention loss.
• Figure 5: Learning with uncertain accurate distance. First Row: The ground truth; Second Row: The hologram; Third Row: The reconstruction with our reverse-attention loss; and Fourth Row: Upper bound of the Autofocusing. The reconstruction uses the precise object distance.

Theorems & Definitions (5)

• Theorem 1
• proof
• Theorem 2
• Lemma 3
• proof