In this paper, we propose a unified algebraic design of the generalized Moreau enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced (LiGME) model. The LiGME model has been established as a framework to construct linearly involved nonconvex regularizers for sparsity (or low-rank) aware estimation, where the design of GME matrix is a key to guarantee the overall convexity of the model. The proposed design is applicable to general linear operators involved in the regularizer of the LiGME model, and does not require any eigendecomposition or iterative computation. We also present an application of the LiGME model with the proposed GME matrix to a group sparsity aware least squares estimation problem. Numerical experiments demonstrate the effectiveness of the proposed GME matrix in the LiGME model.

Contamination of water resources with pathogenic microorganisms excreted in human feces is a worldwide public health concern. Surveillance of fecal contamination is commonly performed by routine monitoring for a single type or a few types of microorganism(s). To design a feasible routine for periodic monitoring and to control risks of exposure to pathogens, reliable statistical algorithms for inferring correlations between concentrations of microorganisms in water need to be established. Moreover, because pathogens are often present in low concentrations, some contaminations are likely to be under a detection limit. This yields a pairwise left-censored dataset and complicates computation of correlation coefficients. Errors of correlation estimation can be smaller if undetected values are imputed better. To obtain better imputations, we utilize side information and develop a new technique, the asymmetric Tobit model which is an extension of the Tobit model so that domain knowledge can be exploited effectively when fitting the model to a censored dataset. The empirical results demonstrate that imputation with domain knowledge is effective for this task.

In wireless links between ground stations and UAVs (Unmanned Aerial Vehicles), wireless signals may be attenuated by obstructions such as buildings. A three-dimensional RSS (Received Signal Strength) map (3D-RSS map), which represents a set of RSSs at various reception points in a three-dimensional area, is a promising geographical database that can be used to design reliable ground-to-air wireless links. The construction of a 3D-RSS map requires higher computational complexity, especially for a large 3D area. In order to sequentially estimate a 3D-RSS map from partial observations of RSS values in the 3D area, we propose a graph Laplacian-based sequential smooth estimator. In the proposed estimator, the 3D area is divided into voxels, and a UAV observes the RSS values at the voxels along a predetermined path. By considering the voxels as vertices in an undirected graph, a measurement graph is dynamically constructed using vertices from which recent observations were obtained and their neighboring vertices, and the 3D-RSS map is sequentially estimated by performing graph Laplacian regularized least square estimation.

Three-dimensional (3D) reconstruction and scene depth estimation from 2-dimensional (2D) images are major tasks in computer vision. However, using conventional 3D reconstruction techniques gets challenging in participating media such as murky water, fog, or smoke. We have developed a method that uses a continuous-wave time-of-flight (ToF) camera to estimate an object region and depth in participating media simultaneously. The scattered light observed by the camera is saturated, so it does not depend on the scene depth. In addition, received signals bouncing off distant points are negligible due to light attenuation, and thus the observation of such a point contains only a scattering component. These phenomena enable us to estimate the scattering component in an object region from a background that only contains the scattering component. The problem is formulated as robust estimation where the object region is regarded as outliers, and it enables the simultaneous estimation of an object region and depth on the basis of an iteratively reweighted least squares (IRLS) optimization scheme. We demonstrate the effectiveness of the proposed method using captured images from a ToF camera in real foggy scenes and evaluate the applicability with synthesized data.

Real-time pulse rate (PR) monitoring based on photoplethysmography (PPG) has been drawn much attention in recent years. However, PPG signal detected under movement is easily affected by random noises, especially motion artifacts (MA), affecting the accuracy of PR estimation. In this paper, a parallel method structure is proposed, which effectively combines wavelet threshold denoising with recursive least squares (RLS) adaptive filtering to remove interference signals, and uses spectral peak tracking algorithm to estimate real-time PR. Furthermore, we propose a parallel structure RLS adaptive filtering to increase the amplitude of spectral peak associated with PR for PR estimation. This method is evaluated by using the PPG datasets of the 2015 IEEE Signal Processing Cup. Experimental results on the 12 training datasets during subjects' walking or running show that the average absolute error (AAE) is 1.08 beats per minute (BPM) and standard deviation (SD) is 1.45 BPM. In addition, the AAE of PR on the 10 testing datasets during subjects' fast running accompanied with wrist movements can reach 2.90 BPM. Furthermore, the results indicate that the proposed approach keeps high estimation accuracy of PPG signal even with strong MA.

The consistent alignment of point clouds obtained from multiple scanning positions is a crucial step for many 3D modeling systems. This is especially true for environment modeling. In order to observe the full scene, a common approach is to rotate the scanning device around a rotation axis using a turntable. The final alignment of each frame data can be computed from the position and orientation of the rotation axis. However, in practice, the precise mounting of scanning devices is impossible. It is hard to locate the vertical support of the turntable and rotation axis on a common line, particularly for lower cost consumer hardware. Therefore the calibration of the rotation axis of the turntable is an important step for the 3D reconstruction. In this paper we propose a novel calibration method for the rotation axis of the turntable. With the proposed rotation axis calibration method, multiple 3D profiles of the target scene can be aligned precisely. In the experiments, three different evaluation approaches are used to evaluate the calibration accuracy of the rotation axis. The experimental results show that the proposed rotation axis calibration method can achieve a high accuracy.

Many autocorrelation-based frequency estimation algorithms have been proposed. However, some of them cannot construct a strict linear prediction (LP) property among the adjacent autocorrelation lags, which affects the estimators' performance. To improve the precision of frequency estimation, two novel autocorrelation based frequency estimation methods of the real sinusoid signal in additive white Gaussian noise (AWGN) are proposed in this paper. Firstly, a simple method is introduced to transform the real sinusoid signal into the noncircular signal. Secondly, the autocorrelation of the noncircular signal is analyzed and a strict LP property is constructed among the adjacent autocorrelation lags of the noncircular signal. Thirdly, the least squares (LS) and reformed Pisarenko harmonic decomposer (RPHD) frameworks are employed to improve estimation accuracy. The simulation results match well with the theoretical values. In addition, computer simulations demonstrate that the proposed algorithm provides high estimation accuracy and good noise suppression capability.

A novel time-series relationship among four consecutive real-valued single-tone sinusoid samples is proposed based on their linear prediction property. In order to achieve unbiased frequency estimates for a real sinusoid in white noise, based on the proposed four-point time-series relationship, a constrained least squares cost function is minimized based on the unit-norm principle. Closed-form expressions for the variance and the asymptotic expression for the variance of the proposed frequency estimator are derived, facilitating a theoretical performance comparison with the existing three-point counterpart, called as the reformed Pisarenko harmonic decomposer (RPHD). The region of performance advantage of the proposed four-point based constrained least squares frequency estimator over the RPHD is also discussed. Computer simulations are conducted to support our theoretical development and to compare the proposed estimator performance with the RPHD as well as the Cramer-Rao lower bound (CRLB).

An improved radiometric calibration algorithm by extending the Mitsunaga and Nayar least-square minimization based algorithm with two major ideas is presented. First, a noise & outlier removal procedure based on the analysis of brightness transfer function is included for improving the algorithm's capability on handling noise and outlier in least-square estimation. Second, an alternative minimization formulation based on weighted least square is proposed to improve the weakness of least square minimization when dealing with biased distribution observations. The performance of the proposed algorithm with regards to two baseline algorithms is demonstrated, i.e. the classical least square based algorithm proposed by Mitsunaga and Nayar and the state-of-the-art rank minimization based algorithm proposed by Lee et al. From the results, the proposed algorithm outperforms both baseline algorithms on both the synthetic dataset and the dataset of real-world images.

A new method for adaptive digital beamforming technique with compressed sensing (CS) for sparse receiving arrays with gain/phase uncertainties is presented. Because of the sparsity of the arriving signals, CS theory can be adopted to sample and recover receiving signals with less data. But due to the existence of the gain/phase uncertainties, the sparse representation of the signal is not optimal. In order to eliminating the influence of the gain/phase uncertainties to the sparse representation, most present study focus on calibrating the gain/phase uncertainties first. To overcome the effect of the gain/phase uncertainties, a new dictionary optimization method based on the total least squares (TLS) algorithm is proposed in this paper. We transfer the array signal receiving model with the gain/phase uncertainties into an EIV model, treating the gain/phase uncertainties effect as an additive error matrix. The method we proposed in this paper reconstructs the data by estimating the sparse coefficients using CS signal reconstruction algorithm and using TLS method toupdate error matrix with gain/phase uncertainties. Simulation results show that the sparse regularized total least squares algorithm can recover the receiving signals better with the effect of gain/phase uncertainties. Then adaptive digital beamforming algorithms are adopted to form antenna beam using the recovered data.

Computing autocorrelation coefficient can effectively reduce the influence of additive white noise, thus estimation precision will be improved. In this paper, an autocorrelation-like function, different from the ordinary one, is defined, and is proven to own better linear predictive performance. Two algorithms for signal model are developed to achieve frequency estimates. We analyze the theoretical properties of the algorithms in the additive white Gaussian noise. The simulation results match with the theoretical values well in the sense of mean square error. The proposed algorithms compare with existing estimators, are closer to the Cramer-Rao bound (CRLB). In addition, computer simulations demonstrate that the proposed algorithms provide high accuracy and good anti-noise capability.

This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.

Most conventional research on target motion analysis (TMA) based on least squares (LS) has focused on performing asymptotically unbiased estimation with inaccurate measurements. However, such research may often yield inaccurate estimation results when only a small set of measurement data is used. In this paper, we propose an accurate TMA method even with a small set of bearing measurements. First, a subset of measurements is selected by a random sample consensus (RANSAC) algorithm. Then, LS is applied to the selected subset to estimate target motion. Finally, to increase accuracy, the target motion estimation is refined through a bias compensation algorithm. Simulated results verify the effectiveness of the proposed method.

An improved beamformer, which uses joint estimation of the reconstructed interference-plus-noise (IPN) covariance matrix and array steering vector (ASV), is proposed. It can mitigate the problem of performance degradation in situations where the desired signal exists in the sample covariance matrix and the steering vector pointing has large errors. In the proposed method, the covariance matrix is reconstructed by weighted sum of the exterior products of the interferences' ASV and their individual power to reject the desired signal component, the coefficients of which can be accurately estimated by the compressed sensing (CS) and total least squares (TLS) techniques. Moreover, according to the theorem of sequential vector space projection, the actual ASV is estimated from an intersection of two subspaces by applying the alternating projection algorithm. Simulation results are provided to demonstrate the performance of the proposed beamformer, which is clearly better than the existing robust adaptive beamformers.

Nonnegative Matrix Factorization (NMF) with sparseness and smoothness constraints has attracted increasing attention. When these properties are considered, NMF is usually formulated as an optimization problem in which a linear combination of an approximation error term and some regularization terms must be minimized under the constraint that the factor matrices are nonnegative. In this paper, we focus our attention on the error measure based on the Euclidean distance and propose a new iterative method for solving those optimization problems. The proposed method is based on the Hierarchical Alternating Least Squares (HALS) algorithm developed by Cichocki et al. We first present an example to show that the original HALS algorithm can increase the objective value. We then propose a new algorithm called the Gauss-Seidel HALS algorithm that decreases the objective value monotonically. We also prove that it has the global convergence property in the sense of Zangwill. We finally verify the effectiveness of the proposed algorithm through numerical experiments using synthetic and real data.

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm is developed to approximate the RLS-based online NMF algorithm with low complexity. The proposed algorithm is evaluated in terms of audio source separation, and the results show that the performance of the proposed algorithms are superior to that of the conventional online NMF algorithm with significantly reduced complexity.

In this letter, we present a novel method for reconstructing continuous data field from scattered point data, which leads to a more characteristic visualization result by volume rendering. The gradient distribution of scattered point data is analyzed for local feature investigation via singular-value decomposition. A data-adaptive ellipsoidal shaped function is constructed as the penalty function to evaluate point weight coefficient in MLS approximation. The experimental results show that the proposed method can reduce the reconstruction error and get a visualization with better feature discrimination.

Much attention has recently been paid to sparsity-aware space-time adaptive processing (STAP) algorithms. The idea of sparsity-aware technology is commonly based on the convex l1-norm penalty. However, some works investigate the lq (0 < q < 1) penalty which induces more sparsity owing to its lack of convexity. We herein consider the design of an lq penalized STAP processor with a generalized sidelobe canceler (GSC) architecture. The lq cyclic descent (CD) algorithm is utilized with the least squares (LS) design criterion. It is validated through simulations that the lq penalized STAP processor outperforms the existing l1-based counterparts in both convergence speed and steady-state performance.

Process variation has become prominent in the advanced CMOS technology, making the timing of fabricated circuits more uncertain. In this paper, we propose a Layout-Aware Path Selection (LAPS) technique to accurately estimate the circuit timing variation from a small set of paths. Three features of paths are considered during the path selection. Experiments conducted on benchmark circuits with process variation simulated with VARIUS show that, by selecting only hundreds of paths, the fitting errors of timing distribution are kept below 5.3% when both spatial correlated and spatial uncorrelated process variations exist.

In this paper, we present the channel estimation (CE) problem in the orthogonal frequency division multiplexing system with offset quadrature amplitude modulation (OFDM/OQAM). Most CE methods rely on the assumption of a low frequency selective channel to tackle the problem in a way similar to OFDM. However, these methods would result in a severe performance degradation of the channel estimation when the assumption is not quite inaccurate. Instead, we focus on estimating the channel impulse response (CIR) itself which makes no assumption on the degree of frequency selectivity of the channels. After describing the main idea of this technique, we present an iterative CE method that does not require zero-value guard symbols in the preamble and consequently improves the spectral efficiency. This is done by the iterative estimation of the unknown transmitted data adjacent to the preamble. Analysis and simulation results validate the efficacy of the proposed method in multipath fading channels.