Phaseless super-resolution in the continuous domain

Phaseless super-resolution refers to the problem of superresolving a signal from only its low-frequency Fourier magnitude measurements. In this paper, we consider the phaseless super-resolution problem of recovering a sum of sparse Dirac delta functions which can be located anywhere in the continuous time-domain. For such signals in the continuous domain, we propose a novel Semidefinite Programming (SDP) based signal recovery method to achieve the phaseless superresolution. This work extends the recent work of Jaganathan et al. [1], which considered phaseless super-resolution for discrete signals on the grid

Christ-Centered Discipleship: a Biblical Concept of Religious Education

Concomitant with increased concern for church growth in the 1950s was a new awareness of the importance of discipleship. From the days of Jesus to the present, the concept of discipleship has changed greatly. The problem of this investigation was to identify a Biblical concept of discipleship. It was hypothesized that the relationship of Jesus with His Heavenly Father was the model for Jesus\u27 discipleship with the Twelve apostles and other disciples. The primary objective was to identify principles form this Christ-centered discipleship that could provide a theoretical framework for Christian religious education. The historical development of the Rabbinic schools revealed a marked departure in Rabbinic discipleship from that of the OT. Moreover, Hellenistic educational practices exerted great influence on Rabbinic schools for more than three centuries. A lexical study of selected Hebrew and Greek terms demonstrates nuances and other significant meanings in words used for discipleship during the pre-Chrisitan era. The Servant Songs of Isaiah revealed four principles of discipleship that Jesus fulfilled as reported in the four Gospels. These four principles of the Servant in the Servant Songs of Isaiah are (1) Divine call, (2) commitment, (3) suffering, and (4) glorification. The relationship of the Father to His Son, Jesus, was the paradigm of the relationship of Jesus to His disciples. He commanded them to follow this same pattern of discipleship. The above four principles were conclusively manifested in the discipleship of the Apostles after Pentecost. The coming of the Paraclete is the fulfillment of the promise of Christ to the Twelve including later disciples that He would remain with them through the Spirit until His second coming. This thesis concludes with several suggestions for their implementation in Christian religious education and recommendations for future study

Super-resolution Line Spectrum Estimation with Block Priors

We address the problem of super-resolution line spectrum estimation of an undersampled signal with block prior information. The component frequencies of the signal are assumed to take arbitrary continuous values in known frequency blocks. We formulate a general semidefinite program to recover these continuous-valued frequencies using theories of positive trigonometric polynomials. The proposed semidefinite program achieves super-resolution frequency recovery by taking advantage of known structures of frequency blocks. Numerical experiments show great performance enhancements using our method.Comment: 7 pages, double colum

Off-The-Grid Spectral Compressed Sensing With Prior Information

Recent research in off-the-grid compressed sensing (CS) has demonstrated that, under certain conditions, one can successfully recover a spectrally sparse signal from a few time-domain samples even though the dictionary is continuous. In this paper, we extend off-the-grid CS to applications where some prior information about spectrally sparse signal is known. We specifically consider cases where a few contributing frequencies or poles, but not their amplitudes or phases, are known a priori. Our results show that equipping off-the-grid CS with the known-poles algorithm can increase the probability of recovering all the frequency components.Comment: 5 pages, 4 figure