An Online Plug-and-Play Algorithm for Regularized Image Reconstruction (1809.04693v1)

Abstract: Plug-and-play priors (PnP) is a powerful framework for regularizing imaging inverse problems by using advanced denoisers within an iterative algorithm. Recent experimental evidence suggests that PnP algorithms achieve state-of-the-art performance in a range of imaging applications. In this paper, we introduce a new online PnP algorithm based on the iterative shrinkage/thresholding algorithm (ISTA). The proposed algorithm uses only a subset of measurements at every iteration, which makes it scalable to very large datasets. We present a new theoretical convergence analysis, for both batch and online variants of PnP-ISTA, for denoisers that do not necessarily correspond to proximal operators. We also present simulations illustrating the applicability of the algorithm to image reconstruction in diffraction tomography. The results in this paper have the potential to expand the applicability of the PnP framework to very large and redundant datasets.

• The paper introduces a novel online Plug-and-Play algorithm for regularized image reconstruction specifically designed for large datasets using subset measurements.
• The paper provides comprehensive convergence analysis for both batch and online PnP-ISTA and classifies denoisers for broader applicability within PnP frameworks.
• The work highlights significant scalability improvements via stochastic gradients and shows promise for rapid processing in fields like dynamic object imaging.

An Analysis of an Online Plug-and-Play Algorithm for Regularized Image Reconstruction

The paper under review presents a novel online Plug-and-Play (PnP) algorithm, specifically designed for regularized image reconstruction, leveraging a subset of measurements at each iteration. This approach is based ultimately on the integration of advanced denoisers within the overarching iterative gradient descent frameworks used for solving imaging inverse problems. This paper pivots on the cornerstone algorithm developed using the iterative shrinkage/thresholding algorithm (ISTA), providing both batch and online variants with novel theoretical convergence analyses.

Key Contributions

The authors introduce a significant advancement with the newly devised online PnP-ISTA algorithm, catering to large datasets that demand processing efficiencies unfeasible under traditional batch processes. The practical utility of the model is underscored by its adaptability to exceedingly large datasets, such as those encountered in diffraction tomography—ample pretext for the proliferation of online methodologies.

The paper highlights several indispensable theoretical contributions:

• Convergence Analysis: A comprehensive convergence analysis for both batch and online iterations of PnP-ISTA is provided. This includes important findings on denoisers that might not traditionally correlate with proximal operators.
• Denoiser Classification: The classification of denoisers as nonexpansive and/or averaged operators is explored, broadening the scope for satisfactory integration within PnP frameworks. These classifications shed light on the proposed scheme's broad applicability and highlight conditions for convergence that extend beyond symmetrical gradient constraints.

Algorithmic Specifics

Underpinning the algorithm's operation are several important elements:

• Data Fidelity and Regularization: These are conventionally balanced using ISTA and ADMM, which avoid stringent differentiation demands through proximal operator usage.
• Scalability: The utilisation of stochastic gradient principles allows for enhanced scalability in image reconstruction. By leveraging only subsets of measurements via a stochastic approximation of the gradient, computational complexity is significantly reduced, thus enhancing practical applicability.

Implications and Potential

The implications of this work are multifold:

1. Scalability Improvements: By truncating batch iterations in favor of partial measurement processing, computational loads are alleviated, significantly bridging the gap between scale and performance potential in imaging tasks.
2. Theoretical Expansion: Through easing traditional convex constraints, this framework broadens theoretical horizons on integrating machine learning-driven components, such as sophisticated denoisers, within proximal frameworks.
3. Practical Application: The results show promise for application in fields necessitating rapid component processing, such as dynamic object imaging, where the data throughput exceeds that of offline methodologies.

Future Perspectives

This paper posits various future research directions:

• Extension to Other Imaging Modalities: Continued exploration of the online PnP algorithm across different image reconstruction tasks presents a promising trajectory, such as 3D medical imaging or dynamic scene reconstruction.
• Theoretical Refinement: Further refinement of convergence theory for more generalized denoiser mappings will continue to enhance the robustness of online applications.
• Algorithmic Integration: Investigating the intersection of such algorithms with deep learning models, potentially by marrying neural network denoisers with generalized PnP protocols, can usher a new frontier in automated imaging pipelines.

In summary, this paper provides a detailed exploration of online PnP algorithm applications to image reconstruction, dissected through a lens of scalability, theoretical depth, and proposed practicality. The shift towards efficient online methods marks a notable step in addressing the computational demands of large-scale inverse imaging problems.