Super-Resolution With Binary Priors: Theory and Algorithms
Super-Resolution With Binary Priors: Theory and Algorithms
复制标题
二元先验的超分辨率：理论和算法
DOI：
10.1109/tsp.2023.3260564
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发表时间：
2023
影响因子：
5.4
通讯作者：
Pal, Piya
中科院分区：
文献类型：
--
作者：
Sarangi, Pulak;Hattori, Ryoma;Komiyama, Takaki;Pal, Piya
超分辨率的问题涉及从与低通滤波器卷积的样本中重建时间/空间局部事件（或尖峰）。不同于以往的作品，利用稀疏性在适当的域，以解决由此产生的不适定问题，本文探讨了超分辨率，其中的尖峰（或源）幅度被假定为二进制值的二进制先验的作用。我们的研究受到神经尖峰去卷积问题的启发，但也适用于其他应用，如混合毫米波通信系统中的符号检测。本文提出了几个理论和算法的贡献，使二进制超分辨率与很少的测量。我们的研究结果表明，二进制约束提供了更强的可识别性保证比稀疏，使我们能够在“极端压缩”制度，其中测量的数量可以显着小于稀疏水平的尖峰。为了确保在这种“极端压缩”状态下的精确恢复，有必要设计精确执行二进制约束而不放松的算法。为了克服随之而来的计算挑战，我们考虑一阶自回归滤波器（出现在神经尖峰去卷积），并利用其特殊的结构。这导致在一个新的配方的超分辨率二进制尖峰恢复方面的二进制搜索在一维。我们进行数值实验，验证我们的理论，也显示了二进制约束的好处，神经尖峰反卷积从真实的钙成像数据集。
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in appropriate domains in order to solve the resulting ill-posed problem, this paper explores the role of binary priors in super-resolution, where the spike (or source) amplitudes are assumed to be binary-valued. Our study is inspired by the problem of neural spike deconvolution, but also applies to other applications such as symbol detection in hybrid millimeter wave communication systems. This paper makes several theoretical and algorithmic contributions to enable binary super-resolution with very few measurements. Our results show that binary constraints offer much stronger identifiability guarantees than sparsity, allowing us to operate in “extreme compression” regimes, where the number of measurements can be significantly smaller than the sparsity level of the spikes. To ensure exact recovery in this “extreme compression” regime, it becomes necessary to design algorithms that exactly enforce binary constraints without relaxation. In order to overcome the ensuing computational challenges, we consider a first order auto-regressive filter (which appears in neural spike deconvolution), and exploit its special structure. This results in a novel formulation of the super-resolution binary spike recovery in terms of binary search in one dimension. We perform numerical experiments that validate our theory and also show the benefits of binary constraints in neural spike deconvolution from real calcium imaging datasets.
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DOI：
10.1109/icassp40776.2020.9054299
发表时间：
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期刊：
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影响因子：
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影响因子：
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