Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure

Characterization of the OCO-2 instrument line shape functions using on-orbit solar measurements

Accurately characterizing the instrument line shape (ILS) of the Orbiting Carbon Observatory-2 (OCO-2) is challenging and highly important due to its high spectral resolution and requirement for retrieval accuracy (0. 25 %) compared to previous spaceborne grating spectrometers. On-orbit ILS functions for all three bands of the OCO-2 instrument have been derived using its frequent solar measurements and high-resolution solar reference spectra. The solar reference spectrum generated from the 2016 version of the Total Carbon Column Observing Network (TCCON) solar line list shows significant improvements in the fitting residual compared to the solar reference spectrum currently used in the version 7 Level 2 algorithm in the O₂ A band. The analytical functions used to represent the ILS of previous grating spectrometers are found to be inadequate for the OCO-2 ILS. Particularly, the hybrid Gaussian and super-Gaussian functions may introduce spurious variations, up to 5 % of the ILS width, depending on the spectral sampling position, when there is a spectral undersampling. Fitting a homogeneous stretch of the preflight ILS together with the relative widening of the wings of the ILS is insensitive to the sampling grid position and accurately captures the variation of ILS in the O₂ A band between decontamination events. These temporal changes of ILS may explain the spurious signals observed in the solar-induced fluorescence retrieval in barren areas

Spectral cube extraction for the VLT/SPHERE IFS: Open-source pipeline with full forward modeling and improved sensitivity

We present a new open-source data-reduction pipeline to reconstruct spectral data cubes from raw SPHERE integral-field spectrograph (IFS) data. The pipeline is written in Python and based on the pipeline that was developed for the CHARIS IFS. It introduces several improvements to SPHERE data analysis that ultimately produce significant improvements in postprocessing sensitivity. We first used new data to measure SPHERE lenslet point spread functions (PSFs) at the four laser calibration wavelengths. These lenslet PSFs enabled us to forward-model SPHERE data, to extract spectra using a least-squares fit, and to remove spectral crosstalk using the measured lenslet PSFs. Our approach also reduces the number of required interpolations, both spectral and spatial, and can preserve the original hexagonal lenslet geometry in the SPHERE IFS. In the case of least-squares extraction, no interpolation of the data is performed. We demonstrate this new pipeline on the directly imaged exoplanet 51 Eri b and on observations of the hot white dwarf companion to HD 2133. The extracted spectrum of HD 2133B matches theoretical models, demonstrating spectrophotometric calibration that is good to a few percent. Postprocessing on two 51 Eri b data sets demonstrates a median improvement in sensitivity of 80% and 30% for the 2015 and 2017 data, respectively, compared to the use of cubes reconstructed by the SPHERE Data Center. The largest improvements are seen for poorer observing conditions. The new SPHERE pipeline takes less than three minutes to produce a data cube on a modern laptop, making it practical to reprocess all SPHERE IFS data.Comment: 17 pages, 11 figures. Software available at: https://github.com/PrincetonUniversity/charis-de

Gemini Frontier Fields: Wide-field Adaptive Optics KsK_s-band Imaging of the Galaxy Clusters MACS J0416.1-2403 and Abell 2744

We have observed two of the six Frontier Fields galaxy clusters, MACS J0416.1-2403 and Abell 2744, using the Gemini Multi-Conjugate Adaptive Optics System (GeMS) and the Gemini South Adaptive Optics Imager (GSAOI). With 0.08"-0.10" FWHM our data are nearly diffraction-limited over a 100"x100" wide area. GeMS/GSAOI complements the Hubble Space Telescope (HST) redwards of 1.6microns with twice the angular resolution. We reach a 5 sigma depth of Ks = 25.6 mag (AB) for compact sources. In this paper we describe the observations, the data processing and the initial public data release. We provide fully calibrated, co-added images matching the native GSAOI pixel scale as well as the larger plate scales of the HST release, adding to the legacy value of the Frontier Fields. Our work demonstrates that even for fields at high galactic latitude, where natural guide stars are rare, current multi-conjugated adaptive optics technology at 8m-telescopes has opened a new window on the distant Universe. Observations of a third Frontier Field, Abell 370, are planned.Comment: Accepted for publication in ApJS; significantly revised compared to the first submissio

Undersampled-Based Modulation Schemes for Optical Camera Communications

Widespread use of white light-emitting diodes and ubiquitous smart devices offer the opportunity to establish VLC, which has become a hot research topic based on the growing number of publications over the last decade. Camera-based VLC, namely OCC, provides many unique features when compared to a single-photodiode-based system, such as the ability to separate incident light in the spatial and color domains. OCC technology represents a promising approach to utilize the benefits of VLC in beyond-5G scenarios and is one of the key technologies of the Internet of Things. Establishing a long communication channel in OCC, as well as non-flickering illumination by using low-frame-rate camera detectors, requires special modulation schemes. This article provides an overview of the principles of three categories of modulation schemes for OCC systems using a low-frame-rate camera detector. In addition, a series of undersampled modulation schemes are proposed and discussed to achieve flicker-free OCC with higher spectral efficiency. In addition, framing structures are designed to solve problems occurring in OCC systems using particular modulation schemes. To evaluate the performance of these modulation schemes, measured bit error rate values are shown. Finally, challenges in the implementation of OCC systems are also outlined

Spatial Multiplexing of QPSK Signals with a Single Radio: Antenna Design and Over-the-Air Experiments

The paper describes the implementation and performance analysis of the first fully-operational beam-space MIMO antenna for the spatial multiplexing of two QPSK streams. The antenna is composed of a planar three-port radiator with two varactor diodes terminating the passive ports. Pattern reconfiguration is used to encode the MIMO information onto orthogonal virtual basis patterns in the far-field. A measurement campaign was conducted to compare the performance of the beam-space MIMO system with a conventional 2-by-?2 MIMO system under realistic propagation conditions. Propagation measurements were conducted for both systems and the mutual information and symbol error rates were estimated from Monte-Carlo simulations over the measured channel matrices. The results show the beam-space MIMO system and the conventional MIMO system exhibit similar finite-constellation capacity and error performance in NLOS scenarios when there is sufficient scattering in the channel. In comparison, in LOS channels, the capacity performance is observed to depend on the relative polarization of the receiving antennas.Comment: 31 pages, 23 figure

Accelerated MRI at 9.4 T with electronically modulated time-varying receive sensitivities

PURPOSE To investigate how electronically modulated time-varying receive sensitivities can improve parallel imaging reconstruction at ultra-high field. METHODS Receive sensitivity modulation was achieved by introducing PIN diodes in the receive loops, which allow rapid switching of capacitances in both arms of each loop coil and by that alter B$_{1}$ $^{-}$ profiles, resulting in two distinct receive sensitivity configurations. A prototype 8-channel reconfigurable receive coil for human head imaging at 9.4T was built, and MR measurements were performed in both phantom and human subject. A modified SENSE reconstruction for time-varying sensitivities was formulated, and g-factor calculations were performed to investigate how modulation of receive sensitivity profiles during image encoding can improve parallel imaging reconstruction. The optimized modulation pattern was realized experimentally, and reconstructions with the time-varying sensitivities were compared with conventional static SENSE reconstructions. RESULTS The g-factor calculations showed that fast modulation of receive sensitivities in the order of the ADC dwell time during k-space acquisition can improve parallel imaging performance, as this effectively makes spatial information of both configurations simultaneously available for image encoding. This was confirmed by in vivo measurements, for which lower reconstruction errors (SSIM = 0.81 for acceleration R = 4) and g-factors (max g = 2.4; R = 4) were observed for the case of rapidly switched sensitivities compared to conventional reconstruction with static sensitivities (SSIM = 0.74 and max g = 3.2; R = 4). As the method relies on the short RF wavelength at ultra-high field, it does not yield significant benefits at 3T and below. CONCLUSIONS Time-varying receive sensitivities can be achieved by inserting PIN diodes in the receive loop coils, which allow modulation of B$_{1}$ $^{-}$ patterns. This offers an additional degree of freedom for image encoding, with the potential for improved parallel imaging performance at ultra-high field