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.

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).

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.

In this letter, a micro-expression recognition method is investigated by integrating both spatio-temporal facial features and a regression model. To this end, we first perform a multi-scale facial region division for each facial image and then extract a set of local binary patterns on three orthogonal planes (LBP-TOP) features corresponding to divided facial regions of the micro-expression videos. Furthermore, we use GSLSR model to build the linear regression relationship between the LBP-TOP facial feature vectors and the micro expressions label vectors. Finally, the learned GSLSR model is applied to the prediction of the micro-expression categories for each test micro-expression video. Experiments are conducted on both CASME II and SMIC micro-expression databases to evaluate the performance of the proposed method, and the results demonstrate that the proposed method is better than the baseline micro-expression recognition method.

In recent years, various applications based on propagation characteristics have been developed. They generally utilize the locality of the fading characteristics of multipath environments. On the other hand, if a received signal at a remote location can be estimated beyond the correlation distance of the multipath fading environment, a wide variety of new applications can be possible. In this paper, we attempt to estimate a received signal at a remote location using the MUSIC method and the least squares method. Based on the plane wave assumption for each arriving wave, multipath environment is analyzed through estimation of the directions of arrival by the MUISC method and the complex amplitudes of the received signals by the least squares method, respectively. We present evaluation results on the estimation performance of the method by computer simulations.

This paper presents a downlink interference mitigation framework for two-tier heterogeneous networks, that consist of spectrum-sharing macrocells and femtocells*. This framework establishes cooperation between the two tiers through two algorithms, namely, the restricted waterfilling (RWF) algorithm and iterative reweighted least squares interference alignment (IRLS-IA) algorithm. The proposed framework models the macrocell-femtocell two-tier cellular system as an overlay cognitive radio system in which the macrocell system plays the role of the primary user (PU) while the femtocell networks play the role of the cognitive secondary users (SUs). Through the RWF algorithm, the macrocell basestation (MBS) cooperates with the femtocell basestations (FBSs) by releasing some of its eigenmodes to the FBSs to do their transmissions even if the traffic is heavy and the MBS's signal to noise power ratio (SNR) is high. Then, the FBSs are expected to achieve a near optimum sum rate through employing the IRLS-IA algorithm to mitigate both the co-tier and cross-tier interference at the femtocell users' (FUs) receivers. Simulation results show that the proposed IRLS-IA approach provides an improved sum rate for the femtocell users compared to the conventional IA techniques, such as the leakage minimization approach and the nuclear norm based rank constraint rank minimization approach. Additionally, the proposed framework involving both IRLS-IA and RWF algorithms provides an improved total system sum rate compared with the legacy approaches for the case of multiple femtocell networks.

Least squares error (LSE) method adopted recursively can be used to track the frequency and amplitude of signals in steady states and kinds of non-steady ones in power system. Taylor expansion is used to give another version of this recursive LSE method. Aided by variable-windowed short-time discrete Fourier transform, recursive LSEs with and without Taylor expansion converge faster than the original ones in the circumstance of off-nominal input singles. Different versions of recursive LSE were analyzed under various states, such as signals of off-nominal frequency with harmonics, signals with step changes, signals modulated by a sine signal, signals with decaying DC offset and additive Gaussian white noise. Sampling rate and data window size are two main factors influencing the performance of method recursive LSE in transient states. Recursive LSE is sensitive to step changes of signals, but it is in-sensitive to signals' modulation and singles with decaying DC offset and noise.

This letter deals with a sparse signal recovery problem and proposes a new algorithm based on the iterative reweighted least squares (IRLS) algorithm. We assume that the non-zero values of a sparse signal is always greater than a given constant and modify the IRLS algorithm to satisfy this assumption. Numerical results show that the proposed algorithm recovers a sparse vector efficiently.