Projection-Based Correction for Enhancing Deep Inverse Networks

• URL: http://arxiv.org/abs/2505.15777v1
• Date: Wed, 21 May 2025 17:28:14 GMT
• Title: Projection-Based Correction for Enhancing Deep Inverse Networks
• Authors: Jorge Bacca,
• Abstract summary: We introduce a projection-based correction method to enhance the inference of deep inverse networks.<n>We theoretically demonstrate that if the recovery model is a well-trained deep inverse network, the solution can be decomposed into range-space and null-space components.
• Score: 3.5534933448684134
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a projection-based correction method to enhance the inference of deep inverse networks by ensuring consistency with the forward model. Specifically, given an initial estimate from a learned reconstruction network, we apply a projection step that constrains the solution to lie within the valid solution space of the inverse problem. We theoretically demonstrate that if the recovery model is a well-trained deep inverse network, the solution can be decomposed into range-space and null-space components, where the projection-based correction reduces to an identity transformation. Extensive simulations and experiments validate the proposed method, demonstrating improved reconstruction accuracy across diverse inverse problems and deep network architectures.

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