arXiv:2606.07257v1 Announce Type: cross Abstract: Phase retrieval - recovering a complex-valued field from intensity measurements - is typically solved using variants of the Gerchberg-Saxton (GS) algorithm, understood as alternating projections between measurement planes. Meanwhile, modern computational imaging increasingly relies on gradient-based optimization and automatic differentiation. Here we show that these two approaches are mathematically identical: the GS magnitude replacement step is exactly a unit gradient descent step on an amplitude least-squares loss. This equivalence enables s
This research published on arXiv highlights a key theoretical equivalence between established and modern computational imaging methods, aligning with ongoing efforts to optimize AI and imaging algorithms.
Understanding the mathematical equivalence between different algorithms can lead to more efficient and robust AI models for complex tasks like phase retrieval, impacting fields from medical imaging to optical computing.
This equivalence allows for cross-pollination of techniques, potentially accelerating development in both traditional computational imaging and gradient-based AI optimization, leading to improved performance or new applications.
- · AI algorithm developers
- · Computational imaging researchers
- · Optical computing industry
Improved performance and broader applicability of phase retrieval algorithms across various high-value industries.
Accelerated innovation in sensor technologies and imaging systems that rely on complex signal processing.
Enhanced AI capabilities in areas requiring precise reconstruction from indirect measurements, potentially impacting fields such as autonomous navigation or materials science.
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Read at arXiv cs.LG