# High Bandwidth-Utilization Digital Holographic Reconstruction Using an Untrained Neural Network
## 6 Conclusions  
We have demonstrated a low-carrier-frequency fringe demodulation method for high-SBU DH imaging. Exploiting phase imaging with an untrained neural network, this approach can increase the SBU of the system's sensor from 9.82% of the quasi-off-axis DH to 53.9% under the slightly off-axis DH system. Specifically, we recognize the artifacts-free phase recovery under the slightly off-axis DH as a nonlinear optimization problem. Then, we skillfully migrate the physical model to the cost function of the DL training process to correct the parameter of the neural network. This process will converge to an optimal state iteratively and will gradually recover the delicate phase details of the object from coarse to fine. Different from previous methods [44; 45; 46] for zero-order suppression in the slightly off-axis system, the proposed method only requires a single hologram. Based on the principle of \"cepstrum\" and homomorphic filtering, the nonlinear filtering [21] and the KK method [22; 23] are proposed to suppress the zero-order term in the SFD. However, these methods inevitably require intensity restrictions on the object and reference beams to satisfy the condition that the object-reference ratio is less than 1 [25]. Moreover, the VHQPI method is proposed to achieve zero-order term suppression in the SFD by adaptively and automatically extracting the background component of the image using uVID. However, such an iterative process of extracting frequency components has certain physical limitations that make it difficult to obtain an exact background component. Although DL provides a good imaging paradigm for QPI, the conventional DL models tend to rely on a large number of the dataset. However, it may be prohibitively laborious and time-consuming for a real-world DH system to collect datasets and generate the corresponding ground truth. A novel scheme was proposed using an untrained neural  
Figure 6: The experiment results of the COS-7 cells under the slightly off-axis DH system. (**a**) The captured hologram. (**b**) The reconstructed phase results based on the FT method. (**c**) The results recovered by our method. (**d**) The spectrum of (**a**), its SBU can reach 31.7% (the blue circle indicates 0-order and the yellow circles indicate \(\pm 1\)-order.). (**e1–e3**) The detailed views of ROI in the phase results recovered by the FT method. (**f1–f3**) The detailed views of ROI in the phase results recovered by the proposed method. network in [31; 32; 33], which fits a complete physical model into a conventional DNN without training beforehand based on a large dataset. Inspired by this, our method is proposed to achieve high-SBU, artifact-free QPI from a single-frame hologram. In addition, we consider that the method can be combined with other techniques in the future, such as optical diffraction tomography [47; 48; 49] and common-path off-axis interferometers [50; 51], etc. Additionally, we envision that the adopted idea of a physics-enhanced DL model in this work can also be enlightening for the diverse computational imaging systems in the future. Conceptualization, Z.L., Y.C. and C.Z. ; methodology, Z.L. and J.S. ; software, Y.J. ; validation, Z.L. and C.Z. ; formal analysis, J.S. and C.Z. ; investigation, Z.L. ; resources, Q.C. and C.Z. ; data curation, Q.S. ; writing--original draft preparation, Z.L. and Y.C. ; writing--review and editing, C.Z., P.G., and J.S. ; visualization, Z.L. ; supervision, Q.C. ; project administration, Q.C. and C.Z. ; funding acquisition, C.Z. and Q.C. All authors have read and agreed to the published version of the manuscript.