L1-norm Constraint Research Articles

L0 norm constraint based external control source allocation for the minimum cost control of directed networks

Locating a pre-given number of key nodes that are connected to external control sources so as to minimize the cost of controlling a directed network ẋ(t)=Ax(t)+Bu(t), known as the minimum cost control problem, is of critical importance. Considering a network consisting of N nodes with M external control sources, the state of art techniques employ iterative searching to determine the input matrix B that characterizes how nodes are connected to external control sources, in a matrix space RN×M. The nodes having M largest values of a defined importance index are selected as key nodes. However, such techniques may suffer from large performance penalty in some networks due to the diversity of real-life networks. To address this outstanding issue, we propose an iterative method, termed “L0-norm constraint based projected gradient method” (LPGM). We probabilistically search the input matrix in each iteration by restricting its L0 norm as a fixed value M, which implies that each control source is always only connected to a single key node during the whole searching process. Simulation results show that the solution always efficiently approaches a suboptimal key node set in a few iterations. These results provide a new point of view regarding the key nodes selection in the minimum cost control of directed networks.

Interpolating seismic data via the POCS method based on shearlet transform

A method based on shearlet transform and the projection onto convex sets with L0-norm constraint is proposed to interpolate irregularly sampled 2D and 3D seismic data. The 2D directional filter of shearlet transform is constructed by modulating a low-pass diamond filter pair to minimize the effect of additional edges introduced by the missing traces. In order to abate the spatial aliasing and control the maximal gap between missing traces for a 3D data cube, a 2D separable jittered sampling strategy is discussed. Finally, numerical experiments on 2D and 3D synthetic and real data with different under-sampling rates prove the validity of the proposed method.

Accelerated 3D blind separation of convolved mixtures based on the fast iterative shrinkage thresholding algorithm for adaptive multiple subtraction

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

Third-order AVO inversion for lamé parameter based on inverse operator estimation algorithm

Various linearized Zoeppritz approximations are often used in the forward modeling of amplitude variation with offset (AVO). However, they are usually limited by the elastic parameters with weak properties contrast. The high contrast situations between layers will cause big errors when linear approximate equations are used. Given this problem, the more precise third-order Zoeppritz approximate equation for velocity and density is derived in this study. Parameter sensitivity analysis illustrates that the third-order approximate equation for velocity and density is not favorable for nonlinear AVO inversion because the equation is extremely insensitive to S-wave velocity. In consideration of the sensitivity of elastic parameters and the poor inversion results, we derived the third-order approximate equation for Lamé parameter. A direct inversion method (Named as inverse operator estimation algorithm) is further used for nonlinear AVO inversion. The L1 norm constraint is considered to improve stability and efficiency during the nonlinear inversion process. The suitability and feasibility of the equation and inversion method can be demonstrated by the synthetic examples. Field data examples show that the inversion results have a good agreement with logging curves.

A Multiple Kernel Learning Model Based on p-Norm.

By utilizing kernel functions, support vector machines (SVMs) successfully solve the linearly inseparable problems. Subsequently, its applicable areas have been greatly extended. Using multiple kernels (MKs) to improve the SVM classification accuracy has been a hot topic in the SVM research society for several years. However, most MK learning (MKL) methods employ L1-norm constraint on the kernel combination weights, which forms a sparse yet nonsmooth solution for the kernel weights. Alternatively, the Lp-norm constraint on the kernel weights keeps all information in the base kernels. Nonetheless, the solution of Lp-norm constraint MKL is nonsparse and sensitive to the noise. Recently, some scholars presented an efficient sparse generalized MKL (L1- and L2-norms based GMKL) method, in which L1 L2 established an elastic constraint on the kernel weights. In this paper, we further extend the GMKL to a more generalized MKL method based on the p-norm, by joining L1- and Lp-norms. Consequently, the L1- and L2-norms based GMKL is a special case in our method when p = 2. Experiments demonstrated that our L1- and Lp-norms based MKL offers a higher accuracy than the L1- and L2-norms based GMKL in the classification, while keeping the properties of the L1- and L2-norms based on GMKL.

L1-norm regularization and wavelet transform: An improved plane-wave destruction method

Seismic diffractions are the specific responses of small-scale inhomogeneities or discontinuous structures in the subsurface, such as faults and cracks, and can be used for locating reservoirs of oil and gas. However, because diffraction energy is much weaker than reflection energy, separating diffractions against the background of strong reflections from seismic data is difficult. In this paper, we propose a regularization method based on the l1-norm constraint to extract seismic diffractions from seismic records in the common-offset gathers. Regularization is a practical method for ill-posed nonlinear problems. The proposed method considers wavelet transform and l1-norm regularization in the plane-wave destruction method, which enhances the stability and accuracy of reflection local slopes. Wavelet transform has multi-level and multi-scale analysis properties and thus it is an effective method for sparse transform. Further, the l1-norm can effectively constrain sparsity properties. Through a synthetic example, the stability of this regularization method is demonstrated to be stronger than that of the conventional plane-wave destruction (PWD) method. Both the numerical simulation and field data application indicate that the proposed regularization method for diffraction extraction is promising and feasible in removing specular reflections and strengthening diffractions.

Double temporal sparsity based accelerated reconstruction of compressively sensed resting-state fMRI

A number of reconstruction methods have been proposed recently for accelerated functional Magnetic Resonance Imaging (fMRI) data collection. However, existing methods suffer with the challenge of greater artifacts at high acceleration factors. This paper addresses the issue of accelerating fMRI collection via undersampled k-space measurements combined with the proposed method based on l1−l1 norm constraints, wherein we impose first l1-norm sparsity on the voxel time series (temporal data) in the transformed domain and the second l1-norm sparsity on the successive difference of the same temporal data. Hence, we name the proposed method as Double Temporal Sparsity based Reconstruction (DTSR) method. The robustness of the proposed DTSR method has been thoroughly evaluated both at the subject level and at the group level on real fMRI data. Results are presented at various acceleration factors. Quantitative analysis in terms of Peak Signal-to-Noise Ratio (PSNR) and other metrics, and qualitative analysis in terms of reproducibility of brain Resting State Networks (RSNs) demonstrate that the proposed method is accurate and robust. In addition, the proposed DTSR method preserves brain networks that are important for studying fMRI data. Compared to the existing methods, the DTSR method shows promising potential with an improvement of 10-12 dB in PSNR with acceleration factors upto 3.5 on resting state fMRI data. Simulation results on real data demonstrate that DTSR method can be used to acquire accelerated fMRI with accurate detection of RSNs.

Robust non-negative sparse graph for semi-supervised multi-label learning with missing labels

In multi-label learning, each instance is assumed to belong to multiple nonexclusive classes among a finite number of candidate categories. Labels are related to certain conceptual space according to their semantic similarities. Most existing approaches that deal with missing labels have the limitations in mining interdependencies among labels in the original incomplete label matrix with missing labels. In addition, semantic gaps are often neglected when features are used to facilitate label recovery. In this paper, we propose a novel label recovery method under a semi-supervised setting. The proposed method can perform label matrix imputation in the labeled space and label matrix prediction in the unlabeled space simultaneously. The semantic structure (label relationships among different instances) and the semantic correlation (label relationships among different labels) are also exploited to increase the robustness to semantic gaps and unreliable label correlations respectively. In formulating the objective function, l1-norm and nonnegative constraints are utilized to capture hidden relational graphs in semantic level and to reveal the annotation structure. An iterative mechanism is introduced to assure all variables are reliable. Intensive simulations were conducted and compared with five widely used multi-label datasets. Obtained results show that the proposed method can achieve highly competitive performance compared to other state-of-art methods.

Non-Convex Sparse and Low-Rank Based Robust Subspace Segmentation for Data Mining.

Parsimony, including sparsity and low-rank, has shown great importance for data mining in social networks, particularly in tasks such as segmentation and recognition. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with convex l1-norm or nuclear norm constraints. However, the obtained results by convex optimization are usually suboptimal to solutions of original sparse or low-rank problems. In this paper, a novel robust subspace segmentation algorithm has been proposed by integrating lp-norm and Schatten p-norm constraints. Our so-obtained affinity graph can better capture local geometrical structure and the global information of the data. As a consequence, our algorithm is more generative, discriminative and robust. An efficient linearized alternating direction method is derived to realize our model. Extensive segmentation experiments are conducted on public datasets. The proposed algorithm is revealed to be more effective and robust compared to five existing algorithms.

Contrast Enhancement Based on Intrinsic Image Decomposition.

In this paper, we propose to introduce intrinsic image decomposition priors into decomposition models for contrast enhancement. Since image decomposition is a highly illposed problem, we introduce constraints on both reflectance and illumination layers to yield a highly reliable solution. We regularize the reflectance layer to be piecewise constant by introducing a weighted ℓ1 norm constraint on neighboring pixels according to the color similarity, so that the decomposed reflectance would not be affected much by the illumination information. The illumination layer is regularized by a piecewise smoothness constraint. The proposed model is effectively solved by the Split Bregman algorithm. Then, by adjusting the illumination layer, we obtain the enhancement result. To avoid potential color artifacts introduced by illumination adjusting and reduce computing complexity, the proposed decomposition model is performed on the value channel in HSV space. Experiment results demonstrate that the proposed method performs well for a wide variety of images, and achieves better or comparable subjective and objective quality compared with the state-of-the-art methods.

Robust coupled dictionary learning with ℓ1-norm coefficients transition constraint for noisy image super-resolution

Conventional coupled dictionary learning approaches are designed for noiseless image super-resolution (SR), but quite sensitive to noisy images. We find that the cause is the commonly used ℓF-norm coefficients transition term. In this paper, we propose a robust ℓ1-norm solution by introducing two sub-terms: LR coefficient sparsity constraint term and HR coefficient conversion term, which are able to prevent the noise transmission from noisy input to output. By incorporating our simple yet effective non-linear model inspired by auto-encoder, the proposed ℓ1-norm dictionary learning achieves a more accurate coefficients conversion. Moreover, to make the coefficients conversion more reliable in the iterative process, we bring the non-local self-similarity constraint to regularize the HR sparse coefficients updates. The improved sparse representation further enhances SR inference on both synthesized noisy and noiseless images. Using standard metrics, we show that results are significantly clearer than state-of-the-arts on noisy images and sharper on denoised images. In addition, experiments on real-world data further demonstrate the superiority of our method in practice.

Seismic acoustic impedance inversion with multi-parameter regularization

Most acoustic impedance sparse inversion methods include two parts: reflectivity inversion and extraction of acoustic impedance from reflectivity. This being the case, the acoustic impedance is easily affected by reflectivity and the value of acoustic impedance at time t = 0, thus may become inaccurate. In this paper, we propose a seismic acoustic impedance inversion method with multi-parameter regularization. In our method, the acoustic impedance is calculated directly from objective functions to ensure the stability and accuracy of results. In addition, the total variation regularization, L1 norm constraint, and initial model constraint are used to make the inversion results better accordant with a priori geological information. Moreover, we use multi-trace inversion to reflect the spatial and temporal correlation of the data. Since the objective function contains several different types of regularization term, we have developed an algorithm based on split Bregman iteration to calculate it. The inversion results of theoretical model and field data show that the proposed method has high inversion precision, strong anti-noise ability and good performance on stratigraphy delineation.

Sparse blind deconvolution based low-frequency seismic data reconstruction for multiscale full waveform inversion

Full waveform inversion (FWI) reconstructs the underground velocity structures by minimizing the data residual between calculated wavefields and observed wavefileds. The conventional FWI usually uses some local optimization algorithms which lead to a strong dependency on initial velocity model. The objective function corresponding to low-frequency data components has less local minima. Reconstructing low-frequency information from recorded seismic data and using it in FWI can reduce cycle-skipping and thus weaken the dependency of inversion process on initial model. In this paper, based on the conventional frequency down-shifting method, we propose a sparse blind deconvolution-convolution low-frequency data reconstruction method, which can simultaneously update the wavelet and reconstruct the low-frequency components. First, we extract the subsurface reflection impulse responses (SRIR) by solving a L1 norm sparse constraint problem using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). Then we test the accuracy of our algorithm, and discuss the effect of wavelet error and noises on the reconstruction result.When the wavelet is inaccurate, we update the amplitude of wavelet by alternately inverting L1 norm constraint and Tikhonov regularization problems, and correct the time-shift error by cross-correlating the direct waves. After that we can get the accurate wavelet and SRIR simultaneously. Then using the reconstructed data successively as observed data, combining it with dynamic random sources and layer-stripping methods, we propose a new strategy for the fast multiscale FWI. We test our method by numerical examples in several cases including blended acquisition cases. The results show that it has good anti-noise property and it can reconstruct valid low-frequency components when the observed data lacking low-frequency information. The example using inaccurate wavelet shows that the blind deconvolution-convolution algorithm is able to obtain accurate wavelet and low-frequency data simultaneously.

Linearized dynamic warping with ℓ1-norm constraint for multi-component registration

Registration of the travel time of PP waves and PS waves on the same temporal coordinate is critical for joint interpretation of multi-component seismic data. We propose an ℓ1-norm minimization approach to register the corresponding amplitude of reflection events in the PP waves and PS waves data. The dynamic warping function is linearized in the ℓ2-norm fitting term, and a sparsity constrained is used to estimate smooth warping functions. The latter is possible by defining the warping function in terms of a cosine basis. Sparsity is used to minimize the number of basis functions that are used to model the warping function. We have also applied a fast iterative soft thresholding algorithm for solving the non-linear registration optimization problem. We apply the linearized dynamic warping approach with ℓ1-norm regularization to a synthetic example and to a field data set from the Shengli Oilfield, China.

LRSSL: predict and interpret drug-disease associations based on data integration using sparse subspace learning.

: Exploring the potential curative effects of drugs is crucial for effective drug development. Previous studies have indicated that integration of multiple types of information could be conducive to discovering novel indications of drugs. However, how to efficiently identify the mechanism behind drug-disease associations while integrating data from different sources remains a challenging problem. : In this research, we present a novel method for indication prediction of both new drugs and approved drugs. This method is based on Laplacian regularized sparse subspace learning (LRSSL), which integrates drug chemical information, drug target domain information and target annotation information. Experimental results show that the proposed method outperforms several recent approaches for predicting drug-disease associations. Some drug therapeutic effects predicted by the method could be validated by database records or literatures. Moreover, with L1-norm constraint, important drug features have been extracted from multiple drug feature profiles. Case studies suggest that the extracted drug features could be beneficial to interpretation of the predicted results. https://github.com/LiangXujun/LRSSL. proteomics@csu.edu.cn. Supplementary data are available at Bioinformatics online.

Spectral extrapolation for ultra-wide band radio frequency super-resolution tumor localization in the breast.

The use of ultra-wide band (UWB) radio frequency (RF) as an alternative to x-ray mammography for the detection and localization of breast tumors has been an area of focused research over the last decade. Unlike x-rays, UWB RF is non-ionizing and poses no risk of inducing cancer in examined patients. However, the reduction in operating frequency of UWB RF compared to x-rays results in much poorer localization when using classical space-time adaptive signal processing. This work investigates the synergistic use of a temporal signal spectrum extrapolation technique and contemporary basis pursuit de-noising (BPDN) beamforming to achieve medically relevant tumor localization accuracy within a heterogeneous simulated breast volume. If the beamforming process is viewed as a matched filtering operation, the spectrum extrapolation technique artificially increases the bandwidth of the received signal to afford much sharper correlations and hence contributing to increased localization accuracy. BPDN also contributes to increased localization accuracy by employing L1-norm constraints which shows marked clutter suppression effects in this context.

Sparse Multipath Channel Estimation Using Norm Combination Constrained Set-Membership NLMS Algorithms

A norm combination penalized set-membership NLMS algorithm with l0 and l1 independently constrained, which is denoted as l0 and l1 independently constrained set-membership (SM) NLMS (L0L1SM-NLMS) algorithm, is presented for sparse adaptive multipath channel estimations. The L0L1SM-NLMS algorithm with fast convergence and small estimation error is implemented by independently exerting penalties on the channel coefficients via controlling the large group and small group channel coefficients which are implemented by l0 and l1 norm constraints, respectively. Additionally, a further improved L0L1SM-NLMS algorithm denoted as reweighted L0L1SM-NLMS (RL0L1SM-NLMS) algorithm is presented via integrating a reweighting factor into our L0L1SM-NLMS algorithm to properly adjust the zero-attracting capabilities. Our developed RL0L1SM-NLMS algorithm provides a better estimation behavior than the presented L0L1SM-NLMS algorithm for implementing an estimation on sparse channels. The estimation performance of the L0L1SM-NLMS and RL0L1SM-NLMS algorithms is obtained for estimating sparse channels. The achieved simulation results show that our L0L1SM- and RL0L1SM-NLMS algorithms are superior to the traditional LMS, NLMS, SM-NLMS, ZA-LMS, RZA-LMS, and ZA-, RZA-, ZASM-, and RZASM-NLMS algorithms in terms of the convergence speed and steady-state performance.

A block parallel ℓ0-norm penalized shrinkage and widely linear affine projection algorithm for adaptive filter

To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel l 0 -SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the l 0 -norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent (DCD) iterations and the parallel processing to deal with the tap-weight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steady-state behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer (DFE), the bite error rate (BER) decreases obviously.

Statistical binary patterns and post-competitive representation for pattern recognition

During the last decade, sparse representations have been successfully applied to design high-performing classification algorithms such as the classical sparse representation based classification (SRC) algorithm. More recently, collaborative representation based classification (CRC) has emerged as a very powerful approach, especially for face recognition. CRC takes advantage of SRC through the notion of collaborative representation, relying on the observation that the collaborative property is more crucial for classification than the l1-norm sparsity constraint on coding coefficients used in SRC. This paper follows the same general philosophy of CRC and its main novelty is the application of a virtual collaborative projection (VCP) routine designed to train images of every class against the other classes to improve fidelity before the projection of the query image. We combine this routine with a method of local feature extraction based on high-order statistical moments to further improve the representation. We demonstrate using extensive experiments of face recognition and classification that our approach performs very competitively with respect to state-of-the-art classification methods. For instance, using the AR face dataset, our method reaches 100% of accuracy for dimensionality 300.

Learning a Class-Specific Dictionary for Facial Expression Recognition

Abstract Sparse coding is currently an active topic in signal processing and pattern recognition. Meta Face Learning (MFL) isatypical sparse coding method and exhibits promising performance for classification. Unfortunately, due to using the l1-norm minimization, MFLis expensive to compute and is not robust enough. To address these issues, this paper proposesafaster and more robust version of MFLwith the l2-norm regularization constraint on coding coefficients. The proposed method is used to learnaclass-specific dictionary for facial expression recognition. Extensive experiments on two popular facial expression databases, i.e., the JAFFEdatabase and the Cohn-Kanade database, demonstrate that our method shows promising computational efficiency and robustness on facial expression recognition tasks.