Comparison of uniform resampling and nonuniform sampling direct-reconstruction methods in k-space for FD-OCT

The nonuniform distribution of interference spectrum in wavenumber k-space is a key issue to limit the imaging quality of Fourier-domain optical coherence tomography(FD-OCT).At present,the reconstruction quality at different depths among a variety of processing methods in k-space is still uncertain.Using simulated and experimental interference spectra at different depths,the effects of common six processing methods including uniform resampling(linear interpolation(LI),cubic spline interpolation(CSI),time-domain interpolation(TDI),and K-B window convolution)and nonuniform sampling direct-reconstruction(Lomb periodogram(LP)and nonuniform discrete Fourier transform(NDFT))on the reconstruction quality of FD-OCT were quantitatively analyzed and compared in this work.The results obtained by using simulated and experimental data were coincident.From the experimental results,the averaged peak intensity,axial resolution,and signal-to-noise ratio(SNR)of NDFT at depth from 0.5 to 3.0mm were improved by about 1.9 dB,1.4 times,and 11.8 dB,respectively,compared to the averaged indices of all the uniform resampling methods at all depths.Similarly,the improvements of the above three indices of LP were 2.0 dB,1.4 times,and 11.7 dB,respectively.The analysis method and the results obtained in this work are helpful to select an appropriate processing method in k-space,so as to improve the imaging quality of FD-OCT.

NOISE AMPLIFICATION ANALYSIS AND COMPARISON OF TWO PERIODIC NONUNIFORM SAMPLING RECONSTRUCTION METHODS USED IN DPCA SAR

General Sampling Expansion Reconstruction Method (GSERM) and Digital Spectrum Reconstruction Method (DSRM), which prove effective to reconstruct azimuth signal of Displaced Phase Center Apertures (DPCA) Synthetic Aperture Radar (SAR) system from its Periodic Non-Uniform Sampling (PNUS) data sequences, would amplify the noise and sidelobe clutter simultaneously in the reconstruction. This paper formulates the relation of the system transfer matrixes of the above two methods, gives the properties, such as periodicity, symmetry, and time-shift property, of their Noise and Sidelobe Clutter Amplification Factor (NSCAF), and discovers that DSRM is more sensitive than GSERM in the white noise environment. In addition, criteria based on initial sampling point analysis for the robust PRF selection are suggested. Computer simulation results support these con-clusions.

Underdetermined direction of arrival estimation with nonuniform linear motion sampling based on a small unmanned aerial vehicle platform

Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.

One step hologram calculation for multi-plane objects based on nonuniform sampling(Invited Paper)

The nonuniform sampling method in hologram plane is proposed to reconstruct objects on multi-plane simultaneously. The hologram is nonuniformly sampled by decomposing it into several parts with various sampling rates. The hologram is calculated based on the nonuniform fast Fourier transform （NUFFT） algorithm. In the experiment, we load this nonuniformly sampled hologram on phases-only spatial light modulator （SLM）, and by illumination with collimated light objects with different sampling rates are reconstructed at different distant planes simultaneously. Both of the numerically simulation and optical experiments are performed to demonstrate the feasibility of our method. The experiment also shows that our proposed nonuniform sampled hologram for multi-plane objects is calculated by only one step, better than conventional method that needs several steps of calculation proportional to the numbers of object planes.

Nonuniform sampling and approximation in Sobolev space from perturbation of the framelet system

The Sobolev space H^(■)(R^(d)),where■>d/2,is an important function space that has many applications in various areas of research.Attributed to the inertia of a measurement instrument,it is desirable in sampling theory to recover a function by its nonuniform sampling.In the present paper,based on dual framelet systems for the Sobolev space pair(H^(s)(R^(d)),H^(-s)(R^(d))),where d/2<s<■,we investigate the problem of constructing the approximations to all the functions in H^(■)(R^(d))by nonuniform sampling.We first establish the convergence rate of the framelet series in(H^(s)(R^(d)),H^(-s)(R^(d))),and then construct the framelet approximation operator that acts on the entire space H^(■)(R^(d)).We examine the stability property for the framelet approximation operator with respect to the perturbations of shift parameters,and obtain an estimate bound for the perturbation error.Our result shows that under the condition d/2<s<■,the approximation operator is robust to shift perturbations.Motivated by Hamm(2015)’s work on nonuniform sampling and approximation in the Sobolev space,we do not require the perturbation sequence to be in■^(α)(Z^(d)).Our results allow us to establish the approximation for every function in H^(■)(R^(d))by nonuniform sampling.In particular,the approximation error is robust to the jittering of the samples.

Random Stabilization of Sampled-data Control Systems with Nonuniform Sampling

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.

Nonuniform sampling delta modulation for digital audio processing

A new digital audio processing system based on Nonuniform Sampling Delta Mod-ulation (NSDM) technique is presented in this paper. The performance of NSDM system is analysed. Theoretical analysis and experimental results have demonstrated that the perfor-manc e of NSDM system used in digital audio is better than that of conventional Linear Delta Modulation (LDM) in terms of coding efficiency, Signal to Quantization-Noise Ratio and dy-namic range.

Research Progress of the Sampling Theorem Associated with the Fractional Fourier Transform

Sampling is a bridge between continuous-time and discrete-time signals,which is import-ant to digital signal processing.The fractional Fourier transform(FrFT)that serves as a generaliz-ation of the FT can characterize signals in multiple fractional Fourier domains,and therefore can provide new perspectives for signal sampling and reconstruction.In this paper,we review recent de-velopments of the sampling theorem associated with the FrFT,including signal reconstruction and fractional spectral analysis of uniform sampling,nonuniform samplings due to various factors,and sub-Nyquist sampling,where bandlimited signals in the fractional Fourier domain are mainly taken into consideration.Moreover,we provide several future research topics of the sampling theorem as-sociated with the FrFT.

A Method to Reconstruct Nth-Order Periodically Nonuniform Sampled Signals

It is well known that nonuniform sampling is usually needed in special signals processing. In this paper, a general method to reconstruct Nth-order periodically nonuniform sampled signals is presented which is also developed to digital domain, and the designs of the digital filters and the synthesis system are given. This paper extends the studies of Kohlenberg, whose work concentrate on the periodically nonuniform sampling of second order, as well as the studies of A.J.Coulson, J.L.Brown, whose work deal with the problems of two-band signals’ Nth-order sampling and reconstruction.