Compressed sensing with structured sparsity and structured acquisition
Compressed sensing with structured sparsity and structured acquisition
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DOI：
10.1016/j.acha.2017.05.005
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发表时间：
2019-03-01
影响因子：
2.5
通讯作者：
Weiss, Pierre
中科院分区：
文献类型：
--
作者：
Boyer, Claire;Bigot, Jeremie;Weiss, Pierre
压缩感知（CS）是磁共振成像（MRI）等应用的一个有吸引力的框架。然而，到目前为止，CS理论提出的传感方案是由随机孤立的测量，这通常是不兼容的物理采集。为了反映成像设备的物理约束，我们引入了测量块的概念：感测方案不再是一组孤立的测量，而是一组可以表示任何任意形状（例如平行或径向线）的测量组。结构化采集测量块容易实现，并提供良好的重建结果在实践中。然而，在这种情况下，很少有结果存在CS重建的理论保证。在本文中，我们推导出新的CS结构化收购和信号满足事先结构稀疏的结果。所得到的结果提供了一个稀疏向量的恢复概率，明确地取决于他们的支持。因此，我们的结果是支持依赖的，并提供了灵活的假设稀疏结构的可能性。此外，结果是绘图相关的，因为我们突出了重建稀疏向量的概率和选择测量块的方式之间的显式依赖性。数值模拟表明，该理论是忠实于实验观察。(C)2017爱思唯尔公司All rights reserved.
Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually incompatible with the physics of acquisition. To reflect the physical constraints of the imaging device, we introduce the notion of blocks of measurements: the sensing scheme is not a set of isolated measurements anymore, but a set of groups of measurements which may represent any arbitrary shape (parallel or radial lines for instance). Structured acquisition with blocks of measurements are easy to implement, and provide good reconstruction results in practice. However, very few results exist on the theoretical guarantees of CS reconstructions in this setting. In this paper, we derive new CS results for structured acquisitions and signals satisfying a prior structured sparsity. The obtained results provide a recovery probability of sparse vectors that explicitly depends on their support. Our results are thus support-dependent and offer the possibility for flexible assumptions on the sparsity structure. Moreover, the results are drawing-dependent, since we highlight an explicit dependency between the probability of reconstructing a sparse vector and the way of choosing the blocks of measurements. Numerical simulations show that the proposed theory is faithful to experimental observations. (C) 2017 Elsevier Inc. All rights reserved.