Non-negative sparse recovery at minimal sampling rate

In cognitive radios (CR), compressive spectrum sensing (CSS) is a promising technique to detect wideband spectrum holes with reduced sampling rate requirement of analog-to-digital converter (ADC). It is implied in compressive sensing (CS) that the minimum sampling rate is determined by the sparsity order of the observed wideband signal. Unfortunately, the sparsity order is previously unknown and dynamically varies. Meanwhile, CS technology fails to work efficiently for the nonsparse spectrum case. For example, the CSS performance degenerates significantly for low signal-to-noise ratio (SNR) scenarios since the observed signal becomes nonsparse in frequency domain. To overcome the above-mentioned challenges, we propose a novel CSS algorithm with temporally-correlated prior knowledge mining (TPKM-CSS) to detect spectrum holes without a prior sparsity order information. The proposed scheme can handle both the sparse and nonsparse spectrum cases. The proposed solution has three contributions: firstly, CR implements multiple parallel sampling simultaneously to acquire wireless spectrum signals, which have a low-rank spectrum matrix. Secondly, the temporal correlation between continuous CS data is further exploited to improve the estimation accuracy of the current spectrum. Finally, the theoretical performance of the proposed TPKM-CSS is evaluated, wherein the cumulative distribution function (CDF) of the spectrum reconstruction error is derived in the closed form. The simulation results show that the proposed scheme works well for both sparse and nonsparse spectrum scenarios. Compared with the CSS schemes that are based on low-rank matrix recovery (LMR-CSS), maximizing correlation (MC), iterative compressive filtering (ICF), or Bayesian CS (BCS), the proposed scheme yields the superior performance in terms of the probability of detection and the probability of false alarm, especially for nonsparse signals. Furthermore, the simulated statistical performance of the spectrum reconstruction error matches well the theoretical CDF curve.

Light field sampling (LFS) theory can properly reduce minimum sampling rate while ensuring that novel views are not distorted for image-based rendering (IBR). The minimum sampling rate is determined by spectral support of light field. The spectral support of light field has studied the influence of the following factors: the minimum depth and the maximum depth, non-Lambertian reflections, whether the scene surfaces are flat, maximum frequency of painted signals. In this paper, we further perfect the light field spectrum analysis from the quantitative description of scene texture information based on the existing spectrum analysis theory. The quantification of texture information can be interactively refined via detected regional entropy. Thus, we can derive a spectral analytical function of light field with respect to texture information. The new function allows the spectral support of light field to be analyzed and estimated for different texture information associated with scene objects. In this way, we limit the spectral analysis problems of light field to those of a simpler signal. We show that this spectral analysis approach can be easily extended to arbitrary scene complexity levels, as we simplify the LFS of complex scenes to a plane. Additionally, the spectral support of light field broadens as the plane texture information becomes more complex. We present experimental results to demonstrate the performance of LFS with texture information, verify our theoretical analysis, and extend our conclusions on the optimal minimum sampling rate.

We study a sampling problem where sampled signals come from a known union of shift-invariant subspaces and the sampling operator is a linear projection of the sampled signals into a fixed shift-invariant subspace. In practice, the sampling operator can be easily implemented by a multichannel uniform sampling procedure. We present necessary and sufficient conditions for invertible and stable sampling operators in this framework, and provide the corresponding minimum sampling rate. As an application of the proposed general sampling framework, we study the specific problem of spectrum-blind sampling of multiband signals. We extend the previous results of Bresler et al. by showing that a large class of sampling kernels can be used in this sampling problem, all of which lead to stable sampling at the minimum sampling rate.

A sampling criterion for a surface reconstruction using structured light patterns is derived in this article. The problem of signal recovery from its samples is addressed, and a salient spatial frequency component of an object is defined for a sampling rate determination. The authors introduce 3D object coordinate extraction from a 2D captured image by employing structured light systems (a set of concentric circular light patterns), without any prior information about an object of interest. To achieve an efficient 3D reconstruction (approximate reconstruction result), a minimal sampling rate, defined as the minimum number of circular patterns to be projected onto the 3D scene, is derived using specific geometric information (e.g., curvature) of an object. This article chiefly deals with theoretical algorithms for efficient 3D scene reconstruction, recognition and other applications of 3D imaging techniques, and the proposed algorithms can be applied to diverse applications in the field of computer vision, 3D graphics, etc.

We consider 2-D multiband signals, with a given bound on their spectral occupancy (the occupied fraction of the area of a bounding box of the spectral support). We propose a universal sampling pattern that guarantees well-conditioned reconstruction of all such signals. Such a universal sampling pattern can asymptotically achieve the Nyquist-Landau (1967) minimal sampling rate, determined by the spectral occupancy. Compared to 'Nyquist' patterns that avoid aliasing, for sparse spectral supports our design offers considerable reduction in sampling rate. Furthermore, we propose algorithms allowing reconstruction to be done blindly-without prior knowledge of the spectral support, other than its bounding box. The results apply to both continuous and discrete-time signals, and directly generalize to M-D. This work extends our analogous results for the 1D case.

A novel method for highly-undersampled Magnetic Resonance Image (MRI) reconstruction is presented. One of the principal challenges faced in clinical MR imaging is the fundamental linear relation between net exam duration and admissible spatial resolution. Increased scan duration diminishes patient comfort while increasing the risk of susceptibility to motion artifact and limits the ability to depict many physiological events at high temporal rates. With the recent development of Compressive Sampling theory, several authors have successfully demonstrated that clinical MR images possessing a sparse representation in some transform domain can be accurately reconstructed even when sampled at rates well below the Nyquist limit by casting the recovery as a convex ℓ₁-minimization problem. While ℓ₁-based techniques offer a sizeable advantage over Nyquist-limited methods, they nonetheless require a modest degree of over-sampling above the true theoretical minimum sampling rate in order to guarantee the achievability of exact reconstruction. In this work, we present a reconstruction model based on homotopic approximation of the ℓ₀ quasi-norm and discuss the ability of this technique to reconstruct undersampled MR images at rates even lower than are achievable than with ℓ₁-minimization and arbitrarily close to the true minimum sampling rate. A semi-implicit numerical solver is presented for efficient numerical computation of the reconstruction process and several examples depicting the capability for accurate MRI reconstructions from highly-undersampled K-space data are presented.

We propose a universal sampling pattern and corresponding reconstruction algorithms that guarantee well-conditioned reconstruction of all multiband signals with a given spectral occupancy bound without prior knowledge of the spectral support. It is shown that such a universal sampling pattern can asymptotically achieve the Nyquist-Landau (1957) minimal sampling rate. Also, the new design method replaces the nonaliasing or packability criterion for a reconstructive sampling pattern with a more lenient criterion, allowing reconstruction of signals aliased by sampling.

The main purpose of this study was to develop an inexpensive, simple, rapid and sensitive chemiluminescence (CL) method for the determination of enrofloxacin (ENRO) using a flow-injection system. This method is based on rapid reduction of Ru(phen)(3)(3+), which is produced in the reaction between Ru(phen)(3)(2+) and acidic Ce(IV) by ENRO, producing strong CL. A central composite design (CCD) was used for optimization of the chemical variables. Regression analysis of the data from the CCD demonstrated that a second-order polynomial model is an adequate description of the surface over the factor limits studied. Optimization using CCD gave approximately four-fold better results than the single-factor-at-a-time method. Under optimal experimental conditions, the CL response was proportional to the concentration of ENRO over a wide range (0.008-3.6 microg/mL) with a correlation coefficient of 0.9986 and a detection limit of 0.003 microg/mL (3sigma). The relative standard deviation for 11 repeated determinations of 0.14 microg/mL ENRO was 4.2%. This method was successfully applied to the analysis of commercial formulations, spiked plasma and spiked poultry tissue. Sample analyses showed good recovery percentages for drugs and spiked plasma (95.1-103.9%). Recovery percentages for spiked poultry tissue were in the range 77.6-87.3%. The minimum sampling rate was 100 samples/h.

We consider the parameter design of a TCP portscan detection scheme with packet sampling. We assume that anomalous hosts infected by worms or bots perform portscan and generate a large number of scanning TCP flows as well as its usual traffic. We regard a flow consisting of SYN packets only (SYN-only flow) as a portscan flow and attempt to detect hosts who generate θ SYN-only flows or more, where θ denotes the threshold. In this framework, we present a method for determining the threshold of sampled SYN-only flows and the minimum sampling rate under the constraints of the predefined false positive and false negative ratios. We conduct sampling experiments with public trace data and demonstrate the effectiveness of our design.

Determination of melamine by flow injection analysis based on chemiluminescence system

A new flow injection chemiluminescence (CL) system was used for the determination of noscapine. This technique is based on the reduction effect of noscapine on the Ru(phen)3(3+), which is produced by reaction between Ru(phen)3(2+) and acidic Ce(IV) solutions, and this rapid reduction produces strong CL. Calibration plots were linear over the range of 3.0 x 10(-7) - 2.0 x 10(-6) mol L(-1) and 2.0 x 10(-6) - 2.0 x 10(-4) mol L(-1). The CL intensity was so high, that it is able to produce a detection limit of 6.6 x 10(-8) M noscapine (3sigma). The relative standard deviation of 2.0 x 10(-6) M noscapine was 1.0% (n=10). The proposed method was successfully applied for the flow injection determination of noscapine in cough and Tonin syrup samples. The results of real sample analyses show good recovery percentages (97.3-102.4%). The minimum sampling rate was 100 samples per hour.

Recently, many image-based modeling and rendering techniques have been successfully designed to render photo-realistic images without the need for explicit 3D geometry. However, these techniques (e.g., light field rendering (Levoy, M. and Hanrahan, P., 1996. In SIGGRAPH 1996 Conference Proceedings, Annual Conference Series, Aug. 1996, pp. 31–42) and Lumigraph (Gortler, S.J., Grzeszczuk, R., Szeliski, R., and Cohen, M.F., 1996. In SIGGRAPH 1996 Conference Proceedings, Annual Conference Series, Aug. 1996, pp. 43–54)) may require a substantial number of images. In this paper, we adopt a geometric approach to investigate the minimum sampling problem for light field rendering, with and without geometry information of the scene. Our key observation is that anti-aliased light field rendering is equivalent to eliminating the “double image” artifacts caused by view interpolation. Specifically, we present a closed-form solution of the minimum sampling rate for light field rendering. The minimum sampling rate is determined by the resolution of the camera and the depth variation of the scene. This rate is ensured if the optimal constant depth for rendering is chosen as the harmonic mean of the maximum and minimum depths of the scene. Moreover, we construct the minimum sampling curve in the joint geometry and image space, with the consideration of depth discontinuity. The minimum sampling curve quantitatively indicates how reduced geometry information can be compensated by increasing the number of images, and vice versa. Experimental results demonstrate the effectiveness of our theoretical analysis.

Shannon / Nyquist sampling theorem indicates that during the sampling process the minimum sample rate must be more than the double of the band of the signal so that we can achieve images without distortion. High-frequency sampling leads to mass data and results in high cost of storage and transmission procedure. Compressed sensing indicates that we can sample data at far below the Nyquist frequency when the signals are sparse or can be represented as sparse on some orthogonal basis, and the signals can be recovered without distortion after some certain recovery algorithms. By this means the cost of storage and transmission can be reduced significantly. Unlike conventional optical imaging process, this paper presents a new imaging method using a Fourier transform lens system, which enables single-exposure and single-aperture compressed imaging. First, the Fourier transformation of image signals is accomplished after they pass through a Fourier transform optical system. Second, sparse sample data can be obtained after the spectrum signals pass the sensor array. The process mentioned above can be interpreted as that using a Fourier matrix and a sparse matrix to complete the measurement of the image signals. Third, we make use of fast iterative threshold recovery algorithm to compute the sampling values and obtain the target image signals. Compared with the conventional imaging methods, in the case of ensuring the image quality, our method can significantly reduce the number of samples, thus greatly reduce the data redundancy. Simulation results indicate that the imaging method proposed can be prospective.

Periodic nonuniform sampling of multiband signals

We propose a simple method for the determination of minimum efficacious sampling rate and sample size in Shewhart-like control charts, a controversial topic both in the academic and industrial fields dealing with Statistical Process Control (SPC). By modeling the control procedure as the sampling of a stochastic process and analyzing data in the frequency realm, it is possible to identify meaningful system time scales and apply the well-known Nyquist–Shannon sampling theorem in order to define conditions for an efficient quality control practice. Such conditions express the minimal requirements for an efficacious monitoring of quality indices, indicating the minimal efficacious sampling rate and the minimal effective size of rational subgroups in Xbar and R (or S) charts, which are useful both in the set-up phase and in the on-line control phase of the Shewhart’s control charts. Results can be applied also to I-MR charts. No statistical assumptions are made on the monitored data; in particular neither statistical independence nor Gaussianity is assumed in the derivation of the results. We focus on continuous processes like those typical in, but not limited to, e.g. refining, chemical processing and mining.