Robust Reconstruction of Imaging Signals under Uncertain Forward Model Parameters using Neural Network Priors

Core Concepts

A novel Moment-Aggregation (MA) framework that can reconstruct imaging signals by considering all candidate parameters of the uncertain forward model simultaneously during the training of a neural network prior.

Abstract

The content discusses the problem of inverse imaging, where the goal is to reconstruct an original image from its compressed measurements. This problem is often ill-posed, as there can be multiple interchangeably consistent solutions. The reconstruction process typically relies heavily on the parameters of the imaging (forward) model, which may not be fully known or may undergo calibration drifts. These uncertainties in the forward model create substantial challenges, as inaccurate reconstructions usually occur when the postulated parameters of the forward model do not fully match the actual ones. To address this issue, the authors propose a novel Moment-Aggregation (MA) framework that is compatible with the popular solution of using a neural network prior. Specifically, the MA framework can reconstruct the signal by considering all candidate parameters of the forward model simultaneously during the update of the neural network. The authors provide a theoretical analysis of the MA framework, demonstrating its convergence properties and similar complexity to reconstruction under the known forward model parameters. The authors conduct proof-of-concept experiments on two applications: compressive sensing and phase retrieval. The results show that the proposed MA framework achieves performance comparable to the forward model with the known precise parameter in reconstruction across various datasets, including MNIST, X-ray, Glas, and MoNuseg, with a PSNR gap of 0.17 to 1.94 compared to the upper bound.

Stats

The measurement y is obtained by applying a forward model with a known parameter A(x0; θ*) to the ground truth data x0, with y = A(x0; θ*) + η, where η is the measurement noise. The set of candidate forward model parameters is Θ = {θ1, ..., θnc}, where nc is the total number of candidates. The objective function is F(x; θi) = 1/2 || y - A(x; θi) ||_2^2, where θi ∈ Θ.

Quotes

"Inverse imaging problems (IIPs) aim to reconstruct a sought-after image x0 ∈ Rn from its measurements y ∈ Rm, where m is often much smaller than n and the observation is typically contaminated by some sort of observation noise η." "It is worth mentioning that one key issue of IIPs is that the quality of signal reconstruction can be severely declined if the designed and implemented parameters of forward models do not match."

Key Insights Distilled From

Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameters

by Xiwen Chen,W... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.02944.pdf

Deeper Inquiries

How can the MA framework be extended to handle more complex imaging models and real-world scenarios beyond the assumptions made in this work?

The MA framework can be extended to handle more complex imaging models and real-world scenarios by incorporating additional factors and considerations into the optimization process. One way to enhance the framework is to introduce adaptive weighting mechanisms for the candidate parameters based on their relevance or reliability in the reconstruction process. This adaptive weighting can help prioritize certain parameters over others, especially when some parameters are known to be more accurate or informative. Furthermore, the MA framework can be extended to incorporate domain-specific knowledge or constraints into the reconstruction process. For example, in medical imaging applications, incorporating anatomical priors or physiological constraints can improve the accuracy of the reconstruction under uncertain forward model parameters. By integrating such domain knowledge, the framework can better guide the optimization process towards more realistic and clinically relevant solutions. Additionally, the MA framework can be enhanced by integrating multi-modal data fusion techniques, where information from different imaging modalities or sources is combined to improve the reconstruction quality. This can be particularly useful in scenarios where multiple types of measurements are available, each with its own set of uncertain parameters. To address real-world scenarios, the MA framework can also be extended to handle dynamic or time-varying forward model parameters. By incorporating adaptive learning mechanisms that can update the candidate parameters over time based on feedback or additional information, the framework can adapt to changing conditions and improve the robustness of the reconstruction process.

What are the potential limitations of the MA framework, and how can they be addressed to further improve the reconstruction performance under uncertain forward model parameters?

One potential limitation of the MA framework is the computational overhead associated with considering multiple candidate parameters during the optimization process. This can lead to increased training time and resource requirements, especially when the number of candidate parameters is large. To address this limitation, optimization strategies such as parallel computing or distributed training can be employed to speed up the convergence of the framework. Another limitation is the assumption of convexity and smoothness in the loss function, which may not always hold true in practical scenarios. To improve the reconstruction performance under uncertain forward model parameters, more sophisticated loss functions that capture the non-linear relationships between the candidate parameters and the reconstruction quality can be explored. This may involve incorporating higher-order terms or regularization techniques to better model the complex error landscape. Furthermore, the MA framework may face challenges in scenarios where the candidate parameters are highly correlated or redundant, leading to suboptimal aggregation of information. To address this, feature selection or dimensionality reduction techniques can be applied to identify the most informative parameters and reduce redundancy in the optimization process. Additionally, the MA framework's performance may be sensitive to the initialization of the neural network and the choice of hyperparameters. Fine-tuning these aspects through extensive experimentation and tuning can help improve the stability and convergence of the framework under uncertain forward model parameters.

What other applications or domains beyond imaging could benefit from the MA framework's ability to handle parameter uncertainty, and how could it be adapted to those contexts?

The MA framework's ability to handle parameter uncertainty can benefit various other applications and domains beyond imaging, such as signal processing, natural language processing, and financial modeling. In signal processing, the framework can be adapted to address signal reconstruction problems with uncertain system parameters, such as audio signal denoising or speech enhancement. In natural language processing, the MA framework can be applied to text generation tasks where the underlying language model parameters are uncertain or variable. By aggregating information from multiple candidate models, the framework can improve the robustness and accuracy of text generation under parameter uncertainty. In financial modeling, the MA framework can be utilized for risk assessment and portfolio optimization under uncertain market conditions. By considering multiple candidate parameters for economic models or risk factors, the framework can provide more reliable predictions and decision-making support in volatile financial markets. To adapt the MA framework to these contexts, domain-specific features and constraints can be incorporated into the optimization process to guide the aggregation of information from candidate parameters. Additionally, specialized loss functions and regularization techniques tailored to the specific application domain can be designed to enhance the reconstruction performance and model accuracy. Collaborations with domain experts and stakeholders can also help tailor the framework to the unique requirements and challenges of each application domain.