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Abstract Advances in compressive sensing (CS) provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with potentially fundamental sample complexity bottlenecks. In particular, tractable algorithms for compressive phase retrieval with sparsity priors have not been able to achieve optimal sample complexity. This has created an open problem in compressive phase retrieval: under generic, phaseless linear measurements, are there tractable reconstruction algorithms that succeed with optimal sample complexity? Meanwhile, progress in machine learning has led to the development of new data‐driven signal priors in the form of generative models, which can outperform sparsity priors with significantly fewer measurements. In this work, we resolve the open problem in compressive phase retrieval and demonstrate that generative priors can lead to a fundamental advance by permitting optimal sample complexity by a tractable algorithm. We additionally provide empirics showing that exploiting generative priors in phase retrieval can significantly outperform sparsity priors. These results provide support for generative priors as a new paradigm for signal recovery in a variety of contexts, both empirically and theoretically. The strengths of this paradigm are that (1) generative priors can represent some classes of natural signals more concisely than sparsity priors, (2) generative priors allow for direct optimization over the natural signal manifold, which is intractable under sparsity priors, and (3) the resulting non‐convex optimization problems with generative priors can admit benign optimization landscapes at optimal sample complexity, perhaps surprisingly, even in cases of nonlinear measurements.
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This content will become publicly available on April 18, 2026
A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts
Abstract Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. This reassembly problem requires understanding the attributes of individual pieces and establishing matches between different pieces. Many approaches also model priors of the underlying complete object. Existing approaches are tightly connected problems of shape segmentation, shape matching, and learning shape priors. We provide existing algorithms in this context and emphasize their similarities and differences to general‐purpose approaches. We also survey the trends from early procedural approaches to more recent deep learning approaches. In addition to algorithms, this survey will also describe existing datasets, open‐source software packages, and applications. To the best of our knowledge, this is the first comprehensive survey on this topic in computer graphics.
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- Award ID(s):
- 2115405
- PAR ID:
- 10593678
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Computer Graphics Forum
- ISSN:
- 0167-7055
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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