Single-shot inline holography using a physics-aware diffusion model: errata

Yunping Zhang; Xihui Liu; Xihui Liu; Edmund Y. Lam

doi:10.1364/OE.525947

Abstract

We present an erratum to our paper [Opt. Express 32, 10444 (2024) [CrossRef] ]. This erratum aims to address an unintentional error in the methodology presented in Part 3.1. The error may lead to confusion among readers, and we provide additional clarification to ensure a comprehensive understanding of the technique. It is important to note that these corrections do not affect the results or conclusions of the original work.

1.

In our paper [1], the $\nabla _{\boldsymbol {v}_{t}}$ should be corrected to $\nabla _{\boldsymbol {x}_{t}}$ in Algorithm 1 and its corresponding schematic figure (Fig. 1) to accurately represent the gradient correction step as

(1)$$\boldsymbol{x}_{t-1} =\boldsymbol{v}_{t}-\rho \nabla_{\boldsymbol{x}_{t}}\left\|\boldsymbol{y}-\mathcal{T}(\hat{\boldsymbol{x}}_{0})\right\|_{2}^{2},$$

where $\hat {\boldsymbol {x}}_{0}$ is a function of $\boldsymbol {x}_{t}$, and $\rho =1/\gamma ^2$ is the stepsize. By doing so, we maximize the likelihood $p(\boldsymbol {y}\,|\, \hat {\boldsymbol {x}}_0)$ of the recorded hologram $\boldsymbol {y}$. It is demonstrated in [2] that an approximation of $p(\boldsymbol {y}\,|\, \boldsymbol {x}_t)$ can be yield using $p(\boldsymbol {y}\,|\, \hat {\boldsymbol {x}}_0)$, with the approximation error quantified using the Jensen gap [3]. Thus, this correction step can be associated with the maximization of the intractable likelihood $p(\boldsymbol {y}\,|\,\boldsymbol {x}_t)$ during the sampling process, which elucidates the rationale behind our correction approach for integrating the physics of the digital holographic imaging system.

Fig. 1. (a) A comparison between the ancestral diffusion step (depicted in black) and our proposed physics-aware diffusion model (PadDH, represented in orange). It involves an intermediate transformation from $\boldsymbol {x}_t$ to $\boldsymbol {v}_{t}$ and further transformation into $\boldsymbol {x}_{t-1}$. (b) A detailed visual depiction of the correction step, illustrating the sequence of transformations from $\boldsymbol {x}_t$ to $\boldsymbol {v}_{t}$ and then to $\boldsymbol {x}_{t-1}$.

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The corresponding corrected version is presented in Fig. 1 and Algorithm 1.

Algorithm 1. Physics-aware diffusion model for digital holographic reconstruction

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References

1. Y. Zhang, X. Liu, and E. Y. Lam, “Single-shot inline holography using a physics-aware diffusion model,” Opt. Express 32(6), 10444–10460 (2024). [CrossRef]

2. H. Chung, J. Kim, M. T. Mccann, et al., “Diffusion posterior sampling for general noisy inverse problems,” in The Eleventh International Conference on Learning Representations (2023).

3. M. DeGroot and M. Schervish, Probability and Statistics, Pearson custom library (Pearson Education, 2013).

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Figures (1)

Fig. 1.

Fig. 1. (a) A comparison between the ancestral diffusion step (depicted in black) and our proposed physics-aware diffusion model (PadDH, represented in orange). It involves an intermediate transformation from

$\boldsymbol {x}_t$

to

$\boldsymbol {v}_{t}$

and further transformation into

$\boldsymbol {x}_{t-1}$

. (b) A detailed visual depiction of the correction step, illustrating the sequence of transformations from

$\boldsymbol {x}_t$

to

$\boldsymbol {v}_{t}$

and then to

$\boldsymbol {x}_{t-1}$

.

View in Article | Download Full Size | PDF

Tables (1)