Sparse recovery of complex phase-encoded velocity images using iterative thresholding

In this paper we propose a new algorithm for reconstructing phase-encoded velocity images of catalytic reactors from undersampled NMR acquisitions. Previous work on this application has employed total variation and nonlinear conjugate gradients which, although promising, yields unsatisfactory, unphysical visual results. Our approach leverages prior knowledge about the piecewise-smoothness of the phase map and physical constraints imposed by the system under study. We show how iteratively regularizing the real and imaginary parts of the acquired complex image separately in a shift-invariant wavelet domain works to produce a piecewise-smooth velocity map, in general. Using appropriately defined metrics we demonstrate higher fidelity to the ground truth and physical system constraints than previous methods for this specific application. © 2013 IEEE.

Model-based compressive Harmonic-Aware Matching Pursuit: An evaluation

This paper addresses devising a reliable model-based Harmonic-Aware Matching Pursuit (HAMP) for reconstructing sparse harmonic signals from their compressed samples. The performance guarantees of HAMP are provided; they illustrate that the introduced HAMP requires less data measurements and has lower computational cost compared with other greedy techniques. The complexity of formulating a structured sparse approximation algorithm is highlighted and the inapplicability of the conventional thresholding operator to the harmonic signal model is demonstrated. The harmonic sequential deletion algorithm is subsequently proposed and other sparse approximation methods are evaluated. The superior performance of HAMP is depicted in the presented experiments. © 2013 IEEE.

Application of fast Pade approximation in simulating photonic crystal nanocavities by FDTD technology

The exact calculation of mode quality factor Q is a key problem in the design of high-Q photonic crystal nanocavity. On the basis of further investigation on conventional Pade approximation, FDM and DFT, Pade approximation with Baker's algorithm is enhanced through introducing multiple frequency search and parabola interpolation. Though Pade approximation is a nonlinear signal processing method and only short time sequence is needed, we find the different length of sequence requirements for 2D and 3D FDTD, which is very important to obtain convergent and accurate results. By using the modified Pade approximation method and 3D FDTD, the 2D slab photonic crystal nanocavity is analyzed and high-Q multimode can be solved quickly instead of large range high-resolution scanning. Monitor position has also been investigated. These results are very helpful to the design of photonic crystal nanocavity devices. (C) 2008 Elsevier B.V. All rights reserved.

Calculation of light delay for coupled microrings by FDTD technique and Pade approximation

The Pade approximation with Baker's algorithm is compared with the least-squares Prony method and the generalized pencil-of-functions (GPOF) method for calculating mode frequencies and mode Q factors for coupled optical microdisks by FDTD technique. Comparisons of intensity spectra and the corresponding mode frequencies and Q factors show that the Pade approximation can yield more stable results than the Prony and the GPOF methods, especially the intensity spectrum. The results of the Prony method and the GPOF method are greatly influenced by the selected number of resonant modes, which need to be optimized during the data processing, in addition to the length of the time response signal. Furthermore, the Pade approximation is applied to calculate light delay for embedded microring resonators from complex transmission spectra obtained by the Pade approximation from a FDTD output. The Prony and the GPOF methods cannot be applied to calculate the transmission spectra, because the transmission signal obtained by the FDTD simulation cannot be expressed as a sum of damped complex exponentials. (C) 2009 Optical Society of America

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Pade approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Pade approximation. The decaying constant beta of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity v(g) as beta = omega/(2Qv(g)). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 10(3) to 10(-4) cm(-1) can be reliably obtained from 8 x 10(3)-item FDTD output with the FDTD computing time of 0.386 ps. And at most 1 ps is required for the mode with the Q-factor of 4 x 10(11) and the decaying rate of 10(-7) cm(-1). In the triangular-lattice photonic crystal slab, a 10(4)-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5 x 10(8) and the decaying rate of 0.05 cm(-1). (c) 2004 Elsevier B.V. All rights reserved.

Method for detecting concurrence without the structural physical approximation by local operations and classical communication

We present a modified method for detecting the concurrence in an arbitrary two-qubit quantum state rho(AB) with local operations and classical communication. In this method, it is not necessary for the two observers to prepare the quantum state rho(AB) by the structural physical approximation. Their main task is to measure four specific functions via two local quantum networks. With these functions they can determine the concurrence and then the entanglement of formation.

Computation of resonant frequencies and quality factors of cavities by FDTD technique and Pade approximation

The finite-difference time domain (FDTD) technique and the Pade approximation with Baker's algorithm are used to calculate the mode frequencies and quality factors of cavities. Comparing with the fast Fourier transformation/Pade method, we find that the Fade approximation and the Baker's algorithm can obtain exact resonant frequencies and quality factors based on a much shorter time record of the FDTD output.

Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Pade approximation

The mode wavelength and quality factor (Q-factor) for resonant modes in optical equilateral triangle resonators (ETR's) are calculated by the finite-difference time-domain (FDTD) technique and the Pade approximation, For an ETR with the side length of 3 mu m and the refractive index of 3.2, we get the mode wavelength interval of about 70 nm and the Q-factor of the fundamental mode over 10(3), The results show that the ETR is suitable to realize single-mode operation, and that the radiation loss in the corner regions of ETR is rather low, In addition, the numerical results of the mode wavelength agree very well with our analytical formula.

Calculation of valence subband structures for strained GaInP/AlGaInP quantum wells without axial approximation

Usually in the calculation of valence subband structure for III-V direct bandgap material, axial approximation had been used in the Luttinger-Kohn model to simplify the computational efforts. In this letter, the valence subband structure for the GaInP/AlGaInP strained and lattice-matched quantum wells was calculated without axial approximation, on the basis of 6x6 Luttinger-Kohn Hamiltonian including strain and spin-orbit splitting effects. The numerical simulation results were presented with help of the finite-difference methods. The calculation results with/without axial approximation were compared and the effect of axial approximation on the valence subband structure was discussed in detail. The results indicated that there was a strong warping in the GaInP valence band, and axial approximation can lead to an error when k was not equal to zero, especially for compressively strained and lattice-matched GaInP/AlGaInP quantum wells.

Calculation of Light Delay by FDTD Technique and Pade Approximation

The time delay for light transmission in a coupled microring waveguide structure is calculated from the phase shift of the transmission coefficient obtained by Pade approximation with Baker's algorithm from FDTD Output. The results show that the Pade approximation is a powerful tool for saving time in FDTD simulation.

Description of a radially polarized Laguerre-Gauss beam beyond the paraxial approximation

Fifth-order corrected expressions for the fields of a radially polarized Laguerre-Gauss (R-TEMn1) laser beams are derived based on perturbative Lax series expansion. When the order of Laguerre polynomial is equal to zero, the corresponding beam reduces to the lowest-order radially polarized beam (R-TEM01). Simulation results show that the accuracy of the fifth-order correction for R-TEMn1 depends not only on the diffraction angle of the beam as R-TEM01 does, but also on the order of the beam. (c) 2007 Optical Society of America.