Sparse Signal Representation Research Articles

SAR Target Recognition via Joint Sparse and Dense Representation of Monogenic Signal

Synthetic aperture radar (SAR) target recognition under extended operating conditions (EOCs) is a challenging problem due to the complex application environment, especially for insufficient target variations and corrupted SAR images in the training samples. This paper proposes a new strategy to solve these problems for target recognition. The SAR images are firstly characterized by multi-scale components of monogenic signal. The generated monogenic features are decomposed to learn a class dictionary and a shared dictionary, which represent the possible intraclass variations information and the common information, respectively. Moreover, a sparse representation of the class dictionary and a dense representation of the shared dictionary are jointly employed to represent a query sample for classification. The validity of the proposed strategy is demonstrated with multiple comparative experiments on moving and stationary target acquisition and recognition (MSTAR) database.

Sparse representation of a non-stationary signal in compressive sensing technique

Przedstawiono zastosowanie techniki oszczednego probkowania do rekonstrukcji sygnalu niestacjonarnego na podstawie skompresowanych probek w dziedzinie czas-czestotliwośc. Zastosowano nadmiarowy algorytm z roznymi slownikami aby znaleźc rzadką reprezentacje sygnalu. Wyniki symulacji potwierdzają, ze zastosowanie oszczednego probkowania pozwala na rekonstrukcje sygnalu niestacjonarnego z malej liczby losowo pobranych probek, z niewielką utratą jakości rekonstrukcji.

Sparse and limited-angle CT image reconstruction using dictionary learning constrained by L1 norm

Reconstructed images from computed tomography (CT) using the algebraic reconstruction technique (ART) and simultaneous ART (SART) algorithms often suffer from obvious artefacts when only sparse and limited-angle projection data are available. Using the ability of dictionary learning (DL) in image feature extraction and sparse signal representation, a new iterative reconstruction algorithm, ART-DL-L1, is proposed to overcome the aforementioned limitations. This new algorithm is based on DL and an L1 norm constraint, combined with ART. An alternate iterative solving strategy based on an approach of 'ART first, then adaptive dictionary learning' is suggested and is explicitly described in a flowchart depicting the ART-DL-L1 algorithm. For both a noisy projection of 360° sparse data and limitedangle data of 120°, simulation reconstruction results from the classic Shepp-Logan image obtained using ART-DL-L1 appear to be better than those obtained using SART and total variation (TV) algorithms and also better than the cutting-edge ART-DL-L2 algorithm. Five evaluation metrics corresponding to the root-mean-square error (RMSE), the mean absolute error (MAE), the peak signal-to-noise ratio (PSNR), the residuals and the structural similarity (SSIM) index are adopted to estimate the reconstruction effect. The results suggest that the five metrics obtained using ART-DL-L1 outperform those obtained using the other three algorithms. The impact of using patches of various sizes played by the DL part in ART-DL-L1 is considered in the simulations and the patch size achieving the best reconstructed image quality is identified in this case as 25 (5 × 5). Overall, the proposed ART-DL-L1 algorithm may reduce artefacts and suppress noise from incomplete noisy projection CT imaging to some degree.

K-SVD: Dictionary Developing Algorithms for Sparse Representation of Signal.

The sparse representation of signal is more interested in recent days. It contains overcomplete dictionaries that provides the signal atom. All signals of sparse explained with the help of linear combination of atom. Our proposed system mainly worked on different types of pursuit algorithm that decompose signal with respect to given dictionary D. In K-SVD algorithm description with the help of K-means algorithm. In analytical manner we developed all the algorithm with the help of calculation of dictionary D and it also apply to various method to get updated data. After correction of data we developed K-SVD algorithm which is adaptable. It also work in future work.

On-grid Adaptive Compressive Sensing Framework for Underdetermined DOA Estimation by Employing Singular Value Decomposition

In the field of Array Signal Processing, the problem of Direction of Arrival (DOA) estimation has attracted colossal attention of researchers in the past few years. The problem refers to estimating the angle of arrival of the incoming signals at the receiver end, from the knowledge of the received signal itself. Generally, an array of antenna/sensors is employed at the receiver for this purpose. In over-determined DOA estimation, the number of signal sources, whose direction needs to be estimated are usually lesser than half the number of antenna array elements, whereas the challenge is to estimate the DOAs in under-determined case, where the signal source number is quiet larger than the number of antenna array elements. This paper tackles such a problem by the application of multiple level nested array. Instead of subspace-based techniques for the estimation, sparse signal representation for Compressive Sensing (CS) framework is used, which eliminates the requirement of prior information about the source number and also the tedious task of computing the inverse of the covariance matrices. In this paper, we propose an adaptive approach for Least Absolute Shrinkage and Selection Operator (LASSO) with reduced number of computations by singular value decomposing of the received signal vector. The outcomes of this paper showcase that the presented algorithm achieves high degree of freedom (DOF), good resolution, minimum root mean square error and less computational complexity with increased speed of estimation.

CS–MMPF‐based weak target detection and tracking with range ambiguity

To address the problem of target detection and tracking with the range ambiguous radar in low signal-to-noise ratio environment, a novel weak target detection and tracking algorithm based on the compressed sensing (CS) and multiple model particle filter (MMPF) is proposed. The general solution is that constructing an over-complete atom dictionary according to the echo model of target, obtaining a sparse representation of the target echo signal with the CS method, and conducting a threshold detection with the obtained atom energy distribution and judge whether a target is present or not firstly; roughly extracting the ambiguous measurement of weak target by resolving the least square problem constrained by one-norm minimisation if a target is present then proposing an ambiguous measurement-based MMPF manoeuvring target tracking method, and realising an effective detection and tracking of manoeuvring weak target in the presence of range measurement ambiguity lastly. Simulation results demonstrate that the proposed method can improve the radar performance of target detection and tracking effectively, and succeeds in range ambiguity resolving.

Indoor Positioning Algorithm Fusing Multi-Source Information

With the development of computer technology, mobile intelligent terminal and wireless local area network (WLAN), the applications of location services have shown significant growth, and much progress has been made both in the applications and researches. According to the actual application requirements, a robust indoor positioning algorithm fusing multi-source information was presented in this paper. Firstly, the methods based on the inertial navigation system (INS) and the received signal strength (RSS) of WLAN were discussed and together with their advantages and disadvantages. Then, in order to further improve the positioning performance, a fusion model based on the sparse signal representation theory was designed to integrate the INS and RSS information, and next the optimization solution approach for the fusion model was deeply discussed. Finally, the simulation experiments were designed and carried out, and the experimental results demonstrated the feasibility and effectiveness of the proposed fusion algorithm.

An Object Recognition Approach for Synthetic Aperture Radar Images

In this paper, an object recognition approach for synthetic aperture radar (SAR) images is addressed, which is based on the enhanced kernel sparse representation of monogenic signal. It consists of two main modules. In the first module, to capture the spatial and spectral properties of a target at the same time, a multi-scale monogenic feature extraction scheme is proposed. In the second module, an enhanced kernel sparse representation-based classifier (KSRC) is designed. Different from the traditional KSRC, in the enhanced KSRC, we first integrate the kernel principal component analysis (KPCA) as well as the kernel fisher discriminant analysis (KFDA) to generate an augmented pseudo-transformation matrix. Then, a new discriminative feature mapping approach is presented by exploiting the augmented pseudo-transformation matrix so that the dimensionality of the kernel feature space can be effectively reduced. At last, the l1 -norm minimization is utilized to calculate the sparse coefficients for a test sample, and thus the inference can be reached in terms of the total reconstruction error. Experimental results on the public moving and stationary target acquisition and recognition dataset (MSTAR) demonstrate that the proposed method achieves high recognition accuracy for SAR automatic target recognition.

Reduced iteration image reconstruction of incomplete projection CT using regularization strategy through Lp norm dictionary learning.

For sparse and limited angle projection Computed Tomography (CT), the reconstructed image usually suffers from considerable artifacts due to undersampled data. To improve image reconstruction quality of sparse and limited angle projection CT, this study tested a novel reconstruction algorithm based on Dictionary Learning (DL) from sparse and limited projections. The study used signal sparse representation and feature extraction to render the DL technology, which is constrained by L2 and Lp norms, respectively. A Lp Norm Dictionary Learning term is suitable for regular term of objective function for CT image reconstruction. This is helpful for solving the objective function by combining algorithm of ART. Based on these features, the new algorithm of ART-DL-Lp is proposed for CT image reconstruction. The alternate solving strategy of the algorithm of "ART first, then adaptive DL" is provided in sequence. The impact on reconstruction results of ART-DL-Lp at different p values (0 < p < 1) is also considered. For non-ideal projections with noise, the digital experiments show that ART-DL-Lp data were superior to those of ART, SART, and ART-DL-L2. Accordingly, the objective evaluation metrics for non-ideal situation of RMSE, MAE, PSNR, Residuals and SSIM are all better than those of contrasted three algorithms. The metrics curves of ART-DL-Lp algorithm are recorded as the best. In both incomplete projection situations, smaller p-value of ART-DL-Lp algorithm induces more close reconstructed images to the original form and better five objective evaluation metrics. Overall, the reconstruction efficiency of the proposed ART-DL-Lp for CT imaging using the noisy incomplete projections outperforms ART, SART and ART-DL-L2 algorithms. For ART-DL-Lp algorithm, lower p-values result in better reconstruction performance.

A Robust Phase-Ambiguity-Immune DOA Estimation Scheme for Antenna Array

A direction-of-arrival (DOA) estimation scheme that is immune to phase ambiguity is proposed for directional uniform circular array in the context of software defined radio based engineering implementation, where phase calibration is often required in multi-channel receiver for high-resolution, multi-source DOA estimation algorithms to work. The proposed scheme makes use of sparse signal representation technique, and is robust in the sense that no phase calibration is required when implemented by multi-channel receiver and can achieve multi-source DOA estimation when single-channel receiver is used. To facilitate the performance evaluation, a Cramer–Rao lower bound to the proposed estimation scheme is derived. Implemented by $\ell _1$ -regularized least squares program, the feasibility of the proposed scheme is validated via simulations.

A Sparse Analysis-Based Single Image Super-Resolution

In the current study, we were inspired by sparse analysis signal representation theory to propose a novel single-image super-resolution method termed “sparse analysis-based super resolution” (SASR). This study presents and demonstrates mapping between low and high resolution images using a coupled sparse analysis operator learning method to reconstruct high resolution (HR) images. We further show that the proposed method selects more informative high and low resolution (LR) learning patches based on image texture complexity to train high and low resolution operators more efficiently. The coupled high and low resolution operators are used for high resolution image reconstruction at a low computational complexity cost. The experimental results for quantitative criteria peak signal to noise ratio (PSNR), root mean square error (RMSE), structural similarity index (SSIM) and elapsed time, human observation as a qualitative measure, and computational complexity verify the improvements offered by the proposed SASR algorithm.

Study on sparse representation and measurement matrices of compressive sensing of plant hyperspectral data for retrieving plant physiological and biochemical parameters

The sparse representation of the original signal and compression of the sparse coefficients in the process of compressive sensing have a large influence on the reconstruction of plant hyperspectral data to retrieve plant physiological and biochemical parameters. In order to compress plant hyperspectral data more effectively, we should retain the non-redundant information of the original plant hyperspectral data which lays a good basis for spectral data recovery. Based on the compressive sensing of plant spectral data, discrete cosine transform (DCT), fast Fourier transform (FFT) and K-singular value decomposition (K-SVD) dictionaries are used to compress and reconstruct the plant spectra at different sampling. After the spectral curve, the error of spectral indices of the reconstructed data and the error of inversion model are evaluated, and experimental results show that the K-SVD dictionary can achieve better sparsity performance than that of the other dictionaries at different sampling rates. Based on the K-SVD dictionary, Gaussian matrix, Bernoulli matrix, partial Fourier matrix, sparse random matrix, Toeplitz matrix, and cycling matrix are used to compress and reconstruct the plant spectra at different sampling rates. Experimental results show that partial Fourier matrix can achieve the better compression performance of the spectral curve, SAM, spectral index error and the reconstructed mean PSNR values than that of the other measurement matrices. Therefore, the K-SVD dictionary and partial Fourier matrix of the compressive sensing show the best reconstructed efficiency.

Wind Turbine Bearing Fault Diagnosis Based on Sparse Representation of Condition Monitoring Signals

An effective way to save the costs for data storage and transmission in bearing fault diagnosis of wind turbines is to use a sparse representation of massive condition monitoring signals. A proper dictionary that is adaptive to the analyzed signal containing time-varying components is a key issue to improve the sparse level in the sparse representation method, which has not been addressed in the literature. This paper explores a new sparse representation method that uses a new time-varying cosine-packet dictionary for the bearing fault diagnosis of wind turbines operating under varying speed conditions. First, the time-varying shaft rotating frequency (SRF) of a wind turbine is estimated from a generator current signal recorded synchronously with the vibration signal. Then, the new dictionary is designed, in which the basic functions, called time-varying cosine packet, change with the SRF. Finally, a sparse coefficient spectrum (SCS) of the vibration envelope signal is constructed by the sparse coefficients of the signal projection on the new dictionary. The merits of the proposed sparse representation method are that the dictionary designed is adaptive to the variations of major frequencies of the vibration signals, and the nonzero sparse coefficients over the dictionary designed have a clear physical meaning, i.e., representing the amplitude weights of the major order components contained in the vibration envelope signals. Therefore, the possible bearing fault characteristic orders can be identified from the SCS of the vibration envelope signal. Laboratory and field test results show that the sparse coefficients obtained by the new sparse representation method are suitable for the representations of the bearing vibration signals and the SCS is effective for bearing fault diagnosis of direct-drive wind turbines.

Feasibility Pump Algorithm for Sparse Representation under Laplacian Noise

The Feasibility Pump is an effective heuristic method for solving mixed integer optimization programs. In this paper the algorithm is adapted for finding the sparse representation of signals affected by Laplacian noise. Two adaptations of the algorithm, regularized and nonregularized, are proposed, tested, and compared against the regularized least absolute deviation (RLAD) model. The obtained results show that the addition of the regularization factor always improves the algorithm. The regularized version of the algorithm also offers better results than the RLAD model in all cases. The Feasibility Pump recovers the sparse representation with good accuracy while using a very small computation time when compared with other mixed integer methods.

SSR2: Sparse signal recovery for single-image super-resolution on faces with extreme low resolutions

Automatic face recognition in the wild still suffers from low-quality, low resolution, noisy, and occluded input images that can severely impact identification accuracy. In this paper, we present a novel technique to enhance the quality of such extreme low-resolution face images beyond the current state of the art. We model the correlation between high and low resolution faces in a multi-resolution pyramid and show that we can recover the original structure of an un-seen extreme low-resolution face image. By exploiting domain knowledge of the structure of the input signal and using sparse recovery optimization algorithms, we can recover a consistent sparse representation of the extreme low-resolution signal. The proposed super-resolution method is robust to noise and face alignment, and can handle extreme low-resolution faces up to 16x magnification factor with just 7 pixels between the eyes. Moreover, the formulation of the proposed algorithm allows for simultaneous occlusion removal capability, a desirable property that other super-resolution algorithms do not possess, to the best of our knowledge. Most importantly, we show that our method generalizes on real-world low-quality surveillance images, showing the potentially big impact this can have in a real-world scenario.

Modeling of temperature dependency of structural waves in an ultrasonic flow measurement system

Abstract Structural waves transmitted solely through the pipe wall influence the accuracy in a clamp-on ultrasonic flow measurement system because of the superposition with the signals of interest. To improve the measurement against temperature variations, an algorithmic compensation of the structural waves using a temperature model is required. This paper proposes a temperature model for structural waves, using the Matching Pursuit method. In the first section, a sparse signal representation is presented to approximate the structural wave signals. The resulting signal coefficients are used to describe the temperature dependency in a linear model. The method is validated using measurements of structural waves in a circular pipe over a temperature range between 20 ° C 20\hspace{0.1667em}^\circ \text{C} and 80 ° C 80\hspace{0.1667em}^\circ \text{C} . Based on these measurements, the accuracy of the approximated temperature model is evaluated and compared against the baseline signal-stretch method.

Off-Grid DOA Estimation for Wideband LFM Signals in FRFT Domain Using the Sensor Arrays

For the direction-of-arrival (DOA) estimators based on sparse signal representation, the feasibility and precision are greatly restricted by the inherent limitation of the predefined spatial discrete grids. In this paper, based on the high aggregation characteristic of wideband linear frequency modulation signals, we derive the modified fractional domain sparse model (MFDSM) in DOA estimation and propose a novel off-grid DOA estimation method via alternating descent iteration (OGDEADI). The simulation results show that our proposed MFDSM-OGDEADI method has enhanced estimation accuracy and better angular resolution in terms of signal-to-noise ratio, angle difference, grid size, and angle bias, and it also has the advantage of being less sensitive to the grid size.

Enhancing MR Image Reconstruction Using Block Dictionary Learning

While representing a class of signals in term of sparsifying transform, it is better to use a adapted learned dictionary instead of using a predefined dictionary as proposed in the recent literature. With this improved method, one can represent the sparsest representation for the given set of signals. In order to ease the approximation, atoms of the learned dictionary can further be grouped together to make blocks inside the dictionary that act as a union of small number of subspaces. The block structure of a dictionary can be learned by exploiting the latent structure of the desired signals. Such type of block dictionary leads to block sparse representation of the given signals which can be good for reconstruction of the medical images. In this article, we suggest a framework for MRI reconstruction based upon block sparsifying transform (dictionary). Our technique develops automatic detection of underlying block structure of MR images given maximum block sizes. This is done by iteratively alternating between updating the block structure of the sparsifying transform (dictionary) and block-sparse representation of the MR images. Empirically it is shown that block-sparse representation performs better for recovery of the given MR image with minimum errors.

Sparse-View Reconstruction in Dental Computed Tomography by Using a Dictionary-Learning Based Method

In this study, we investigated sparse-view reconstruction in dental computed tomography (DCT) by using a dictionary-learning (DL)-based method to reduce excessive radiation dose to patients. In sparse-view DCT, only a small number (< 100) of projections, far less than what is required by the Nyquist sampling theory, are acquired from the imaging system and used for image reconstruction. DL is a representation learning theory that aims to find a sparse representation of the input signal in the form of a linear combination of basic elements (or atoms). We implemented a DL-based reconstruction algorithm and performed a systematic simulation and an experiment to evaluate the algorithm’s effectiveness for sparse-view reconstruction in DCT. DCT images were reconstructed using the three sparse-view projections of P30, P40, and P60, and their image qualities were quantitatively evaluated in terms of the intensity profile, the universal quality index, and the peak signal-to-noise ratio. The hardware system used in the experiment consisted of an X-ray tube, which was run at 90 kVp and 40 mA, and a flat-panel detector with a 388-μm pixel size. Our simulation and experimental results indicate that the DL-based method significantly reduced streak artifacts in the sparse-view DCT reconstruction when using P40, thus maintaining image quality.

Перспективные методы цифровой обработки многомерных сигналов на основе применения нерегулярных сеток

The article considers sparse representation of signals based on using irregular meshes, which is one of prospective lines in digital processing of multidimensional signals. Application of irregular meshes has been seen for several decades as a promising field of investigations opening the possibility of using high efficiency of representing a signal carrier in combination with well-developed approximation methods used in solving boundary-value problems. However, lack of tools suitable for solving typical digital signal processing problems with the use of irregular meshes (e.g., for computing orthogonal discrete transforms) had resulted in that any noticeable and practically significant results are lacking in this area. Nevertheless, the recent years have seen a growth of interest in using irregular meshes. The article presents the results of investigations in this field that were carried out at the MPEI Chair for Computers, Systems and Networks. Matters concerned with generation of irregular meshes adapted to the specific features of multidimensional signals are addressed. Algorithms intended for carrying out interpolation, for making a shift from a regular carrier (a uniform regular mesh) to an irregular one, and for computing discrete transformations for a signal with an irregular carrier are presented. Solutions for arranging intellectual signal processing, such as pattern recognition and motion detection, are suggested.