2020/11/12 by Laurent Jacques, Jacques, Laurent, Thomas Feuillen +1
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2011.06499
openalex publication_date 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover such a signal if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the signal sparsity. Our approach consists in recasting the (non-linear) PO-CS scheme as a linear compressive sensing model. We built it from a signal normalization constraint and a phase-consistency constraint. Practically, we achieve stable and robust signal direction estimation from the basis pursuit denoising program. Numerically, robust signal direction estimation is reached at about twice the number of measurements needed for signal recovery in compressive sensing.