Research On Approaches And Applications To Compressive Sensing Sparse Signal Recovery From Magnitude/Phase Measurement

With the emergence of compressed sensing(CS) theory, more and more researchers exploit structural information(i.e., sparse characteristics) of signals to reconstruct signals, recently. The complete theoretical foundation has been established. And a number of practical sparse signal reconstruction approaches are also be developed, which are widely used to solve many problems in the field of signal and information processing. However, as an extension of CS theory, how to reconstruct signal or to estimate signal parameters with magnitude-only information or phase-only information is addressed under the assumption that signal is sparse in the paper. Namely, magnitude-only signal reconstruction issue or phase-only signal reconstruction issue. It is also an active but difficult topic in current CS community. As just magnitude-only measurement sample or phase-only measurement sample obtained in our reasureach, which means there is no magnitude or phase of observed signal, which makes that existed sparse signal recovery approaches cannot be directly applied to solve magnitude-only signal reconstruction problems or phase-only signal reconstruction problems. Therefore, it’s very important to develop new approaches that are suitable for magnitude-only sparse signal(MoSS) reconstruction and phase-only sparse signal(PoSS) reconstruction. In this paper, based on magnitude and phase of signal being of different sparse distributed mode, we exploit sparsity as a priori information to recover signal. We do a thorough research on magnitude/ phase-only sparse signal reconstructed approach and its application from different aspects which are direct compressible sparse signals, indirect compressible sparse signals, semi-sparse signal, and large-scale sparse signals.The research on MoSS reconstructed approach and its application includes three aspects. First, for the sparse signal, we study how to use magnitude-only measurement information to reconstruct the original signal. Qusi-LASSO MoSS reconstruction approach and direct compressible MoSS reconstruction approach are studied, separately. and an indirect compressible Mo SS reconstruction approach is further proposed. Second, for the semi-sparse signal(i.e., amplitude of signal is sparse but phase not), we studied the problem of semi-sparse signal reconstruction under different scenarios. With sparse phase constraint, we propose three MoSS reconstruction approaches based on existing iteration algorithm(i.e., mixed domain observation MoSS reconstruction approach, MoSS reconstruction approach with multiple observation planes, MoSS reconstruction approach with mask perturbations). Third, for large-scale sparse signals, using the relationships between signal power spectral density function and autocorrelation function of signal, we propos a MoSS reconstruction approach based on autocorrelation function of signal. The proposed approach can be carried out MoSS reconstruction from single measured plane but multiple measurements, which is suitable for large-scale MoSS reconstruction problem.The research on phase-only sparse signal(PoSS) reconstructed approach and its application includes two aspects. On the one hand, for the PoSS reconstruction approach and application, it reveals that phase-only measurement sample reserve important information about original signal. It also reveals that it is sufficient to reconstruct the original signal with phase-only samples within a constant ambiguity. We discuss the relationship between existing 1-bit CS technology and PoSS reconstruction and study the PoSS reconstruction approach based on 1-bit CS. On the other hand, for a sparse frequency estimation problem, we propose a phase-only frequency estimation approach with iterative hard threshold(POFEA-IHT). Meanwhile, for the drawback of the proposed approach, we also propos an modified phase-only frequency estimation approach(POFEA-M). POFEA-M makes up the drawback of PODEA-IHT. Besides, by introducing sparse feature of signal, we extend the earlier work about phase-only signal reconstruction approaches.Finally, it should be noted that the MoSS reconstruction approaches and PoSS reconstruction approaches are developed rapidly in recent years. It is a very hot research direction. More and more researchers have focused on this field. Research on MoSS reconstruction approaches and PoSS reconstruction approaches in this paper is not only developed existing compressive sampling signal process theory and approaches, but also promoted the popularization and application of these approaches in radio astronomy, optical wave front sensing, electronic surveillance and other fields. Research on MoSS reconstruction and PoSS reconstruction are significant for relevant scientific research and engineering practice.