Painless Reconstruction from Magnitudes of Frame Coefficients
Painless Reconstruction from Magnitudes of Frame Coefficients
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DOI：
10.1007/s00041-009-9065-1
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发表时间：
2009-08-01
影响因子：
1.2
通讯作者：
Edidin, Dan
中科院分区：
文献类型：
--
作者：
Balan, Radu;Bodmann, Bernhard G.;Edidin, Dan
本文的目标是开发根据帧系数大小进行信号重建的快速算法。这个问题对于信号处理的多个研究领域都很重要，特别是语音识别技术以及量子理论中的状态断层扫描。我们提出了与有限维实数或复数希尔伯特空间中的射影二维设计相关的紧框架的线性重建算法。此类帧的示例是两个均匀帧和相互不偏的基数，其中包括离散的线性调频。使用这些帧进行重建所需的操作数量最多随着希尔伯特空间维度的立方次方增长。此外，我们提出了一种非常有效的算法，它可以对 d 维希尔伯特空间进行 d 次操作的重构。
The goal of this paper is to develop fast algorithms for signal reconstruction from magnitudes of frame coefficients. This problem is important to several areas of research in signal processing, especially speech recognition technology, as well as state tomography in quantum theory. We present linear reconstruction algorithms for tight frames associated with projective 2-designs in finite-dimensional real or complex Hilbert spaces. Examples of such frames are two-uniform frames and mutually unbiased bases, which include discrete chirps. The number of operations required for reconstruction with these frames grows at most as the cubic power of the dimension of the Hilbert space. Moreover, we present a very efficient algorithm which gives reconstruction on the order of d operations for a d-dimensional Hilbert space.