2013/10/04 by Mehmet Akçakaya, Akçakaya, Mehmet, Vahid Tarokh +1
Biochemistry, Genetics and Molecular Biology · Materials Science · Physics and Astronomy · #Advanced Electron Microscopy Techniques and Applications #Advanced X-ray Imaging Techniques #Electron and X-Ray Spectroscopy Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1310.1351
openalex publication_date 2013/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of sparse phase retrieval, where a k-sparse signal \bf x ∈ \mathbb Rn \textrm (or \mathbb Cn\textrm) is measured as \bf y = |\bf Ax|, where \bf A ∈ \mathbb Rm × n \textrm (or \mathbb Cm × n\textrm respectively) is a measurement matrix and |⋅| is the element-wise absolute value. For a real signal and a real measurement matrix \bf A, we show that m = 2k measurements are necessary and sufficient to recover \bf x uniquely. For complex signal \bf x ∈ \mathbb Cn and \bf A ∈ \mathbb Cm × n, we show that m = 4k-2 phaseless measurements are sufficient to recover \bf x. It is known that the multiplying constant 4 in m = 4k-2 cannot be improved.