Complex Approximate Message Passing with Non-separable Denoising
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911616625278976 |
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| author | Kunde, Vishnu Teja Mirri, Alessandro Chamberland, Jean-Francois Paolini, Enrico |
| author_facet | Kunde, Vishnu Teja Mirri, Alessandro Chamberland, Jean-Francois Paolini, Enrico |
| contents | Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced matrix AMP, complex AMP, and AMP for non-separable functions independently, a unified state evolution theory for complex AMP with non-separable denoisers has been lacking. This article fills that gap by establishing state evolution in the setting of complex, non-separable denoising functions. The proposed approach constructs an augmented real-valued system that lifts the problem to a higher-dimensional space, then recovers the complex domain through a many-to-one canonical transformation. Under this construction, the Onsager correction naturally involves Wirtinger derivatives, and the resulting state evolution reduces to scalar complex recursions despite the non-separable structure of the denoisers. The framework extends to the matrix-valued setting, accommodating multiple feature vectors simultaneously. This generalization enables AMP to exploit joint structural constraints, such as simultaneous group and element sparsity, in complex-valued recovery problems. The complex sparse group least absolute shrinkage and selection operator (LASSO) serves as a key instantiation, motivated by preamble detection in Orthogonal Time-Frequency Space (OTFS)-based unsourced random access. Numerical experiments confirm that state evolution accurately predicts performance and show that complex non-separable denoising can produce significant gains over separable and real-valued alternatives. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_21115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Complex Approximate Message Passing with Non-separable Denoising Kunde, Vishnu Teja Mirri, Alessandro Chamberland, Jean-Francois Paolini, Enrico Signal Processing Applications Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced matrix AMP, complex AMP, and AMP for non-separable functions independently, a unified state evolution theory for complex AMP with non-separable denoisers has been lacking. This article fills that gap by establishing state evolution in the setting of complex, non-separable denoising functions. The proposed approach constructs an augmented real-valued system that lifts the problem to a higher-dimensional space, then recovers the complex domain through a many-to-one canonical transformation. Under this construction, the Onsager correction naturally involves Wirtinger derivatives, and the resulting state evolution reduces to scalar complex recursions despite the non-separable structure of the denoisers. The framework extends to the matrix-valued setting, accommodating multiple feature vectors simultaneously. This generalization enables AMP to exploit joint structural constraints, such as simultaneous group and element sparsity, in complex-valued recovery problems. The complex sparse group least absolute shrinkage and selection operator (LASSO) serves as a key instantiation, motivated by preamble detection in Orthogonal Time-Frequency Space (OTFS)-based unsourced random access. Numerical experiments confirm that state evolution accurately predicts performance and show that complex non-separable denoising can produce significant gains over separable and real-valued alternatives. |
| title | Complex Approximate Message Passing with Non-separable Denoising |
| topic | Signal Processing Applications |
| url | https://arxiv.org/abs/2604.21115 |