Joint Sparsity Constraints Research Articles

Efficient and Fast Joint Sparse Constrained Canonical Correlation Analysis for Fault Detection.

The canonical correlation analysis (CCA) has attracted wide attention in fault detection (FD). To improve the detection performance, we propose a new joint sparse constrained CCA (JSCCCA) model that integrates the l2,0 -norm joint sparse constraints into classical CCA. The key idea is that JSCCCA can fully exploit the joint sparse structure to determine the number of extracted variables. We then develop an efficient alternating minimization algorithm using the improved iterative hard thresholding and manifold constrained gradient descent method. More importantly, we establish the convergence guarantee with detailed analysis. Finally, we provide extensive numerical studies on the simulated dataset, the benchmark Tennessee Eastman process, and a practical cylinder-piston process. In some cases, the computing time is reduced by 600 times, and the FD rate is increased by 12.62% compared with classical CCA. The results suggest that the proposed approach is efficient and fast.

Accelerated dynamic MR imaging with joint balanced low-rank tensor and sparsity constraints.

Dynamic magnetic resonance imaging (DMRI) is an essential medical imaging technique, but the slow data acquisition process limits its furtherdevelopment. By exploiting the inherent spatio-temporal correlation of MR images, low-rank tensor based methods have been developed to accelerate imaging. However, the tensor rank used by these methods is defined by an unbalanced matricization scheme, which cannot capture the global correlation of DMR data efficiently during the reconstructionprocess. In this paper, an effective reconstruction model is proposed to achieve accurate reconstruction by using the tensor train (TT) rank defined by a well-balanced matricization scheme to exploit the hidden correlation of DMR data and combining sparsity. Meanwhile, the ket augmentation (KA) technology is introduced to preprocess the DMR data into a higher-order tensor through block structure addressing, which further improves the ability of TT rank to explore the local information of the image. In order to solve the proposed model, the alternating direction method of multipliers (ADMM) is used to decompose the optimization problem into several unconstrainedsubproblems. The performance of the proposed method was validated on the 3D DMR image dataset by using different sampling trajectories and sampling rates. Extensive numerical experiments demonstrate that the reconstruction quality of the proposed method is superior to several state-of-the-art reconstructionmethods. The proposed method successfully utilizes the TT rank to explore the global correlation of DMR images, enabling more detailed information of the image to be captured. Besides, with the sparse priors, the proposed method can further improve the overall reconstruction quality for highly undersampled MRimages.

Learning Sparse Kernel CCA With Graph Priors for Nonlinear Process Monitoring

Process monitoring (PM) is important for improving product quality and ensuring plant safety in industrial systems. Recently, canonical correlation analysis (CCA)-based PM has shown excellent performance. The core idea is to first seek the relationship between two sets of process variables via CCA, then construct a residual generator and determine test statistics, and finally achieve the best monitoring. However, the global and local structure of process variables is not fully exploited. In this article, we propose a new nonlinear PM approach called joint sparse constrained kernel CCA and graph learning (JSKCCA-GL) by incorporating joint sparse kernel CCA (JSKCCA) and graph priors. Technically, imposing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{{2},{0}}$ </tex-math></inline-formula> -norm joint sparse constraints can capture the global row-wise structure, and embedding the graph Laplacian priors can preserve the local structured variable correlation information. Furthermore, an efficient alternating minimization algorithm is developed by integrating least squares and iterative hard thresholding (IHT). The superiority of the proposed JSKCCA-GL is extensively verified on the benchmark Tennessee Eastman process (TEP) and a practical cylinder-piston assembly (CPA) of marine diesel engines. In particular, the fault detection rate (FDR) values for unknown-type faults in the TEP have been improved by around 16.10% on average.

Markov chain-based frequency correlation processing algorithm for wideband DOA estimation

For wideband direction-of-arrival (DOA) estimation, a Markov Chain-based frequency correlation processing algorithm is proposed in the sparse Bayesian learning (SBL) framework, called the MC-FC-SBL algorithm. The algorithm adopts a new frequency-domain structural correlation prior model, which can be adaptively changed to accommodate multi-wideband sources scenarios with different frequency characteristics. Specifically, the MC-FC-SBL algorithm separates the amplitudes and supports of the sparse coefficients through the spike-and-slab model, and judges the frequency correlation by the consistency of the supports at adjacent frequency points. The support prior is represented by a Gaussian mixture model, and the switching between the supports at adjacent frequency points is simulated by a Markov chain. The MC-FC-SBL algorithm performs the DOA estimation in the SBL framework to determine the adaptive prior of each coefficient by evaluating the appropriate frequency-correlation structural pattern. In addition, the MC-FC-SBL algorithm is processed in the real-domain, and the real and imaginary parts of complex signal are regarded as multi-snapshot data to implement joint sparse constraints, which can reduce the computational complexity and improve the algorithm performance. Numerical simulations demonstrate that the MC-FC-SBL algorithm is superior to the existing algorithms for wideband DOA estimation, and the results of field experiments show that this algorithm is still effective when the source is weak.

Abnormal Dynamic Recognition of Space Targets From ISAR Image Sequences With SSAE-LSTM Network

Abnormal dynamics awareness of space targets is critical for space surveillance. With the intrinsic range-Doppler projection mechanism, an inverse synthetic aperture radar (ISAR) image sequence naturally has crucial potential for abnormal dynamics interpretation on uncooperative targets. In this paper, we develop an automated deep neural network architecture for abnormal dynamic recognition of space targets from ISAR image sequences. With the accommodation of the stacked sparse autoencoder (SSAE) network joint sparsity constraint, the geometrical feature flow of an ISAR image sequence is learned to represent the target dynamics concisely. Then, the abnormal dynamic recognition is turned into a sequential classification task by exploiting the encoded feature flow through the long-short time memory (LSTM) network. Extensive experiment results confirm the superiority of the proposal in both precision and efficiency aspects.

Seismic inversion with L2,0-norm joint-sparse constraint on multi-trace impedance model

Impedance inversion of post-stack seismic data is a key technology in reservoir prediction and characterization. Compared to the common used single-trace impedance inversion, multi-trace impedance simultaneous inversion has many advantages. For example, it can take lateral regularization constraint to improve the lateral stability and resolution. We propose to use the L2,0-norm of multi-trace impedance model as a regularization constraint in multi-trace impedance inversion in this paper. L2,0-norm is a joint-sparse measure, which can not only measure the conventional vertical sparsity with L0-norm in vertical direction, but also measure the lateral continuity with L2-norm in lateral direction. Then, we use a split Bregman iteration strategy to solve the L2,0-norm joint-sparse constrained objective function. Next, we use a 2D numerical model and a real seismic data section to test the efficacy of the proposed method. The results show that the inverted impedance from the L2,0-norm constraint inversion has higher lateral stability and resolution compared to the inverted impedance from the conventional sparse constraint impedance inversion.

4DGolden-Angle Radial MRI at Subsecond Temporal Resolution.

Intraframe motion blurring, as a major challenge in free-breathing dynamic MRI, can be reduced if high temporal resolution can be achieved. To address this challenge, this work proposes a highly accelerated 4D (3D + time) dynamic MRI framework with subsecond temporal resolution that does not require explicit motion compensation. The method combines standard stack-of-stars golden-angle radial sampling and tailored GRASP-Pro (Golden-angle RAdial Sparse Parallel imaging with imProved performance) reconstruction. Specifically, 4D dynamic MRI acquisition is performed continuously without motion gating or sorting. The k-space centers in stack-of-stars radial data are organized to guide estimation of a temporal basis, with which GRASP-Pro reconstruction is employed to enforce joint low-rank subspace and sparsity constraints. This new basis estimation strategy is the new feature proposed for subspace-based reconstruction in this work to achieve high temporal resolution (e.g., subsecond/3D volume). It does not require sequence modification to acquire additional navigation data, it is compatible with commercially available stack-of-stars sequences, and it does not need an intermediate reconstruction step. The proposed 4D dynamic MRI approach was tested in abdominal motion phantom, free-breathing abdominal MRI, and dynamic contrast-enhanced MRI (DCE-MRI). Our results have shown that GRASP-Pro reconstruction with the new basis estimation strategy enables highly-accelerated 4D dynamic imaging at subsecond temporal resolution (with five spokes or less for each dynamic frame per image slice) for both free-breathing non-DCE-MRI and DCE-MRI. In the abdominal phantom, better image quality with lower root mean square error and higher structural similarity index was achieved using GRASP-Pro compared with standard GRASP. With the ability to acquire each 3D image in less than 1 s, intraframe respiratory blurring can be intrinsically reduced for body applications with our approach, which eliminates the need for explicit motion detection and motion compensation.

Multicomponent MR fingerprinting reconstruction using joint-sparsity and low-rank constraints.

To develop an efficient algorithm for multicomponent MR fingerprinting (MC-MRF) reconstructions directly from highly undersampled data without making prior assumptions about tissue relaxation times and expected number of tissues. The proposed method reconstructs MC-MRF maps from highly undersampled data by iteratively applying a joint-sparsity constraint to the estimated tissue components. Intermediate component maps are obtained by a low-rank multicomponent alternating direction method of multipliers (MC-ADMM) including the non-negativity of tissue weights as an extra regularization term. Over iterations, the used dictionary compression is adjusted. The proposed method (k-SPIJN) is compared with a two-step approach in which image reconstruction and multicomponent estimations are performed sequentially and tested in numerical simulations and in vivo by applying different undersampling factors in eight healthy volunteers. In the latter case, fully sampled data serves as the reference. The proposed method shows improved precision and accuracy in simulations compared with a state-of-art sequential approach. Obtained in vivo magnetization fraction maps for different tissue types show reduced systematic errors and reduced noise-like effects. Root mean square errors in estimated magnetization fraction maps significantly reduce from 13.0% 5.8% with the conventional, two-step approach to 9.6% 3.9% and 9.6% 3.2% with the proposed MC-ADMM and k-SPIJN methods, respectively. Mean standard deviation in homogeneous white matter regions reduced significantly from 8.6% to 2.9% (two step vs. k-SPIJN). The proposed MC-ADMM and k-SPIJN reconstruction methods estimate MC-MRF maps from highly undersampled data resulting in improved image quality compared with the existing method.

Gradient-echo-train-based sub-millisecond periodic event encoded dynamic imaging with random (k, t)-space undersampling: k-t get-SPEEDI.

PurposeThe gradient‐echo‐train‐based Sub‐millisecond Periodic Event Encoded Dynamic Imaging (get‐SPEEDI) technique provides ultrahigh temporal resolutions (∼0.6 ms) for detecting rapid physiological activities, but its practical adoption can be hampered by long scan times. This study aimed at developing a more efficient variant of get‐SPEEDI for reducing the scan time without degrading temporal resolution or image quality.MethodsThe proposed pulse sequence, named k‐t get‐SPEEDI, accelerated get‐SPEEDI acquisition by undersampling the k‐space phase‐encoding lines semi‐randomly. At each time frame, k‐space was fully sampled in the central region whereas randomly undersampled in the outer regions. A time‐series of images was reconstructed using an algorithm based on the joint partial separability and sparsity constraints. To demonstrate the performance of k‐t get‐SPEEDI, images of human aortic valve opening and closing were acquired with 0.6‐ms temporal resolution and compared with those from conventional get‐SPEEDI.Resultsk‐t get‐SPEEDI achieved a 2‐fold scan time reduction over the conventional get‐SPEEDI (from ∼6 to ∼3 min), while achieving comparable SNRs and contrast‐to‐noise ratio (CNRs) for visualizing the dynamic process of aortic valve: SNR/CNR ≈ 70/38 vs. 73/39 in the k‐t and conventional get‐SPEEDI scans, respectively. The time courses of aortic valve area also matched well between these two sequences with a correlation coefficient of 0.86.ConclusionsThe k‐t get‐SPEEDI pulse sequence was able to half the scan time without compromising the image quality and ultrahigh temporal resolution. Additional scan time reduction may also be possible, facilitating in vivo adoptions of SPEEDI techniques.

Elastic Impedance Simultaneous Inversion for Multiple Partial Angle Stack Seismic Data with Joint Sparse Constraint

Elastic impedance (EI) inversion for partial angle stack seismic data is a key technology in seismic reservoir prediction within the oil and gas industry. EI inversion provides a consistent framework to invert partial angle stack seismic data, just as the AI inversion does for post-stack data. The commonly used EI inversion process is angle by angle. Hence, the inverted EI for different angles may be nonconforming, especially for the seismic data with a low signal-to-noise ratio. This paper proposes to simultaneously invert multiple partial angle stack seismic data to obtain EI for different angles at once. To obtain conformable EI, we used the joint sparse constraint on the reflection coefficients for different angles. Then, the objective function for simultaneous EI inversion was constructed. Next, synthetic seismic data profiles with three different angles were used to show the superiority of the proposed EI inversion method compared to the conventional method. At last, a real seismic data line was used to test the feasibility of the proposed method in practice. The inversion results of synthetic data and real data showed that it provides an effective new alternative method to estimate EI from partial stack seismic data.

Robust Latent Common Subspace Learning for Transferable Feature Representation

This paper proposes a novel robust latent common subspace learning (RLCSL) method by integrating low-rank and sparse constraints into a joint learning framework. Specifically, we transform the data from source and target domains into a latent common subspace to perform the data reconstruction, i.e., the transformed source data is used to reconstruct the transformed target data. We impose joint low-rank and sparse constraints on the reconstruction coefficient matrix which can achieve following objectives: (1) the data from different domains can be interlaced by using the low-rank constraint; (2) the data from different domains but with the same label can be aligned together by using the sparse constraint. In this way, the new feature representation in the latent common subspace is discriminative and transferable. To learn a suitable classifier, we also integrate the classifier learning and feature representation learning into a unified objective and thus the high-level semantics label (data label) is fully used to guide the learning process of these two tasks. Experiments are conducted on diverse data sets for image, object, and document classifications, and encouraging experimental results show that the proposed method outperforms some state-of-the-arts methods.

Rolling Bearing Weak Fault Feature Extraction under Variable Speed Conditions via Joint Sparsity and Low-Rankness in the Cyclic Order-Frequency Domain

Rolling bearings are critical to the normal operation of mechanical systems, which often undergo time-varying working conditions. When the local defects appear on a rolling bearing, the transient impulses will generate and be covered by the strong background noise. Therefore, extracting the rolling bearing weak fault feature with time-varying speed is critical to mechanical system diagnosis. A weak fault feature extraction strategy of rolling bearing under time-varying working conditions is proposed. Firstly, the order-frequency spectral correlation (OFSC) is computed for transferring the measured signal into a higher dimensional space. Then, the joint sparsity and low-rankness constraint is imposed on OFSC to detect the time-varying faulty characteristics. An algorithm in the alternating direction method of multipliers (ADMM) framework is derived. Finally, the enhanced envelope order spectrum (EEOS) is applied to further detect the defective features, which can make the fault features more obvious. The feasibility of the proposed method is confirmed by simulations and an experimental case.

Task-driven joint dictionary learning model for multi-view human action recognition

Traditional self-similarity matrices (SSMs) show outstanding performance in multi-view human action recognition except when the view change becomes large enough. To address this problem, a joint dictionary learning (JDL) algorithm based on joint sparse constraint is presented for trading off the contribution to the sparse features from different views. Unfortunately, the dictionaries and classifiers are trained separately. To enhance the performance of the JDL method, the dictionaries and classifiers can be trained simultaneously in this paper. A task-driven joint dictionary learning model (TJDL) is formulated under the joint sparse constraint. In TJDL, the view-shared dictionary, view-specific dictionaries, linear transformation matrices, action classifiers, view-shared sparse codes, and view-specific sparse codes are learned jointly by a coordinate descent algorithm. Finally, the experimental results over three benchmark datasets show that the proposed TJDL algorithm can achieve superior performance, compared to the recent state-of-the-art methods.

Toward Moving Target Detection in Through-the-Wall Radar Imaging

With the advances in radar technology, through-the-wall radar imaging (TWRI) has become a viable sensing modality that can allow fire-and-rescue personnel, police, and military forces to detect, localize, and identify targets behind opaque obstacles. Many of the existing TWRI approaches detect either stationary or moving targets but not both of them simultaneously. In this article, a method is proposed to detect both stationary and moving targets from a sequence of radar signals. The proposed method decomposes the 3-D radar data, i.e., frequency, space, and time data into a low-rank tensor and two sets of sparse images. One set of images comprises the stationary targets, and the other set of images contains the moving targets. Wall clutter removal and target detection are formulated into an optimization problem regularized by tensor low-rank, joint sparsity, and total variation constraints. Then, an alternating direction technique is developed to reconstruct the sets of stationary and moving target images. Experiments using simulated and real radar signals are conducted. The experimental results illustrate the effectiveness of the proposed method to detect and separate the stationary and moving targets into a pair of sparse images.

Double Regression‐Based Sparse Unmixing for Hyperspectral Images

Sparse unmixing has attracted widespread attention from researchers, and many effective unmixing algorithms have been proposed in recent years. However, most algorithms improve the unmixing accuracy at the cost of large calculations. Higher unmixing accuracy often leads to higher computational complexity. To solve this problem, we propose a novel double regression‐based sparse unmixing model (DRSUM), which can obtain better unmixing results with lower computational complexity. DRSUM decomposes the complex objective function into two simple formulas and completes the unmixing process through two sparse regressions. The unmixing result of the first sparse regression is added as a constraint to the second. DRSUM is an open model, and we can add different constraints to improve the unmixing accuracy. In addition, we can perform appropriate preprocessing to further improve the unmixing results. Under this model, a specific algorithm called double regression‐based sparse unmixing via K‐means (DRSUMK−means) is proposed. The improved K‐means clustering algorithm is first used for preprocessing, and then we impose single sparsity and joint sparsity (using l2,0 norm to control the sparsity) constraints on the first and second sparse unmixing, respectively. To meet the sparsity requirement, we introduce the row‐hard‐threshold function to solve the l2,0 norm directly. Then, DRSUMK−means can be efficiently solved under alternating direction method of multipliers (ADMM) framework. Simulated and real data experiments have proven the effectiveness of DRSUMK−means.

Distributed Compressed Sensing of Hyperspectral Images According to Spectral Library Matching

The ever-increasing resolution puts tremendous pressure to the onboard hyperspectral imaging system. Compressed sensing technology is one of the important ways to solve this problem. Distributed compressed sensing was proposed to exploit both intra- and inter-correlation structures of hyperspectral images. However, the implementation method of distributed compressed sampling has not been reported, and the joint sparsity reconstruction algorithm cannot achieve excellent image reconstruction performance. In this paper, a distributed compressed sampling strategy inspired by distributed compressed video sensing and optical implementation model are proposed to collect compressed hyperspectral data. In the image reconstruction process, we discard the direct application of the joint sparsity constraint on the data itself. Instead, we explore the estimation method of abundance and endmember with the help of the existing spectral library. Then, the images are recovered by applying the linear mixing model of hyperspectral. The comparison experiments of various schemes show that the proposed compressed sensing scheme has an obvious advantage in reconstruction performance under the low sampling rate. The proposed compressed sensing scheme has great potential in a high-compression ratio onboard hyperspectral imaging system.

Model-based reconstruction for simultaneous multi-slice mapping using single-shot inversion-recovery radial FLASH.

To develop a single-shot multi-slice mapping method by combing simultaneous multi-slice (SMS) excitations, single-shot inversion-recovery (IR) radial fast low-angle shot (FLASH), and a nonlinear model-based reconstruction method. SMS excitations are combined with a single-shot IR radial FLASH sequence for data acquisition. A previously developed single-slice calibrationless model-based reconstruction is extended to SMS, formulating the estimation of parameter maps and coil sensitivities from all slices as a single nonlinear inverse problem. Joint-sparsity constraints are further applied to the parameter maps to improve precision. Validations of the proposed method are performed for a phantom and for the human brain and liver in 6 healthy adult subjects. Phantom results confirm good accuracy and precision of the simultaneously acquired multi-slice maps in comparison to single-slice references. In vivo human brain studies demonstrate the better performance of SMS acquisitions compared to the conventional spoke-interleaved multi-slice acquisition using model-based reconstruction. Aside from good accuracy and precision, the results of 6 healthy subjects in both brain and abdominal studies confirm good repeatability between scan and re-scans. The proposed method can simultaneously acquire maps for 5 slices of a human brain ( ) or 3 slices of the abdomen ( ) within 4 seconds. The IR SMS radial FLASH acquisition together with a nonlinear model-based reconstruction enable rapid high-resolution multi-slice mapping with good accuracy, precision, and repeatability.

Myelin water imaging from multi-echo [formula omitted] MR relaxometry data using a joint sparsity constraint

Demyelination is the key pathological process in multiple sclerosis (MS). The extent of demyelination can be quantified with magnetic resonance imaging by assessing the myelin water fraction (MWF). However, long computation times and high noise sensitivity hinder the translation of MWF imaging to clinical practice. In this work, we introduce a more efficient and noise robust method to determine the MWF using a joint sparsity constraint and a pre-computed B1+-T2 dictionary.A single component analysis with this dictionary is used in an initial step to obtain a B1+ map. The T2 distribution is then determined from a reduced dictionary corresponding to the estimated B1+ map using a combination of a non-negativity and a joint sparsity constraint.The non-negativity constraint ensures that a feasible solution with non-negative contribution of each T2 component is obtained. The joint sparsity constraint restricts the T2 distribution to a small set of T2 relaxation times shared between all voxels and reduces the noise sensitivity.The applied Sparsity Promoting Iterative Joint NNLS (SPIJN) algorithm can be implemented efficiently, reducing the computation time by a factor of 50 compared to the commonly used regularized non-negative least squares algorithm. The proposed method was validated in simulations and in 8 healthy subjects with a 3D multi-echo gradient- and spin echo scan at 3 ​T. In simulations, the absolute error in the MWF decreased from 0.031 to 0.013 compared to the regularized NNLS algorithm for SNR ​= ​250. The in vivo results were consistent with values reported in literature and improved MWF-quantification was obtained especially in the frontal white matter. The maximum standard deviation in mean MWF in different regions of interest between subjects was smaller for the proposed method (0.0193) compared to the regularized NNLS algorithm (0.0266). In conclusion, the proposed method for MWF estimation is less computationally expensive and less susceptible to noise compared to state of the art methods. These improvements might be an important step towards clinical translation of MWF measurements.

Learning Hybrid Representation by Robust Dictionary Learning in Factorized Compressed Space.

In this paper, we investigate the robust dictionary learning (DL) to discover the hybrid salient low-rank and sparse representation in a factorized compressed space. A Joint Robust Factorization and Projective Dictionary Learning (J-RFDL) model is presented. The setting of J-RFDL aims at improving the data representations by enhancing the robustness to outliers and noise in data, encoding the reconstruction error more accurately and obtaining hybrid salient coefficients with accurate reconstruction ability. Specifically, J-RFDL performs the robust representation by DL in a factorized compressed space to eliminate the negative effects of noise and outliers on the results, which can also make the DL process efficient. To make the encoding process robust to noise in data, J-RFDL clearly uses sparse L2, 1-norm that can potentially minimize the factorization and reconstruction errors jointly by forcing rows of the reconstruction errors to be zeros. To deliver salient coefficients with good structures to reconstruct given data well, J-RFDL imposes the joint low-rank and sparse constraints on the embedded coefficients with a synthesis dictionary. Based on the hybrid salient coefficients, we also extend J-RFDL for the joint classification and propose a discriminative J-RFDL model, which can improve the discriminating abilities of learnt coefficients by minimizing the classification error jointly. Extensive experiments on public datasets demonstrate that our formulations can deliver superior performance over other state-of-the-art methods.

A Novel Multi-Feature Joint Learning Method for Fast Polarimetric SAR Terrain Classification

Polarimetric synthetic aperture radar (PolSAR) image classification is one of the most important study areas for PolSAR image processing. Many kinds of PolSAR features can be extracted for PolSAR image classification, such as the scattering, polarimetric or image features. However, it is difficult to improve the classification accuracy of PolSAR images by using all these low-level features directly, since they may conflict with each other for classification. Hence, how to joint learn these low-level features to obtain high-level discriminating features is a challenging task. To solve this problem, a novel fast multi-feature joint learning method(fMF-JLC) is proposed for PolSAR image classification. The proposed method extract three kinds of low-level features of PolSAR data at first. Then, a multi-feature joint sparse representation model(MF-JSR) is proposed by designing joint sparse constraints on the extracted features above. Moreover, the joint sparse features are further compressed to overcome the dimension curse and acquire semantic features by the topic model. By this way, the low-level features are fused and discriminating high-level features are acquired. However, the pixel-wise feature learning method is time consuming. To speed the proposed method, a superpixel-based fast learning method is designed by involving the contextual relationship. Experiments are taken on three sets of real PolSAR data with different sensors and bands, and several compared methods are used to verify the effectiveness of the proposed method. The experimental results illustrate that the proposed method can obtain better performance than the state-of-art methods, especially for the heterogenous areas.