Data-Consistent Learning of Inverse Problems

• URL: http://arxiv.org/abs/2601.12831v1
• Date: Mon, 19 Jan 2026 08:41:12 GMT
• Title: Data-Consistent Learning of Inverse Problems
• Authors: Markus Haltmeier, Gyeongha Hwang,
• Abstract summary: Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability.<n>DC networks address this gap by enforcing the measurement model within the network architecture.<n>This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning.
• Score: 3.160733772636691
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Inverse problems are inherently ill-posed, suffering from non-uniqueness and instability. Classical regularization methods provide mathematically well-founded solutions, ensuring stability and convergence, but often at the cost of reduced flexibility or visual quality. Learned reconstruction methods, such as convolutional neural networks, can produce visually compelling results, yet they typically lack rigorous theoretical guarantees. DC (DC) networks address this gap by enforcing the measurement model within the network architecture. In particular, null-space networks combined with a classical regularization method as an initial reconstruction define a convergent regularization method. This approach preserves the theoretical reliability of classical schemes while leveraging the expressive power of data-driven learning, yielding reconstructions that are both accurate and visually appealing.

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