Research On Feature Extraction Of Image Based On Robust Principal Component Analysis

In the field of image processing and pattern recognition,the ability to capture the key information of images will directly affect the subsequent recognition accuracy,so feature extraction is an important technology.In recent years,with the rapid development of optical acquisition equipment,more and more high-dimensional images have been presented into view.When processing those high-dimensional data,researchers will face the problem of small sample to some extent,that is,the number of samples is far less than the number of variables;Meanwhile,the acquired image will inevitably be interfered by noise information,which will bring negative effects on the feature extraction performance,leading to the inaccurate recognition results.Recently,the robust principal component analysis(PCA)method has made great progress in suppressing the noise information of high-dimensional small sample data.However,most of this kind of methods abandon the inherent valuable properties of PCA,such as rotational invariance and solutions related to the covariance matrix,simply changing the distance measurement method to improve the robustness.Based on the above problems,we decided to focus on one-dimensional vector(1D)and two-dimensional matrix(2D)robust PCA methods to effectively improve the recognition ability of images in practical applications.The specific innovations are summarized as follows:First,to solve the problem that robust PCA cannot capture the important features of image accurately in noisy environment,we proposed the feature extraction method based on triangle short side relationship PCA.On the basis of selecting the flexible l2,p-norm as the distance metric,the method reasonably realizes the maximized variance and minimized reconstruction error simultaneously by maximizing the difference between the two short sides of the triangle,which not only improves the robustness but also enhances the universality.Furthermore,the computational efficiency of the method is taken into account to avoid an obvious synchronous change in complexity and robustness.Extensive experimental results show that the proposed method has excellent robustness for images containing noise information.Second,in the image feature extraction task,the above methods ignore the consideration of manifold geometry which may be embedded between pixels.However,the existing robust PCA with manifold structure cannot minimize the reconstruction error under the interference of noise.To solve these problems,we proposed the feature extraction method based on local invariant joint tangent angle PCA,which uses the l2,1-norm to act on both the cost function part to protect the data global geometry and the regularization part to protect the data manifold geometry,which not only improves the robustness but also ensures the rotational invariance of the low-dimensional representation.Moreover,the relationship between reconstruction error and variance is explicitly introduced in the cost function of the model to maximize its performance in the data reconstruction stage.Experimental results on several image datasets with different noise information show that the proposed method has excellent feature extraction ability.Third,when using robust PCA for image analysis,the input image matrix needs to be vectorized in advance,which will inevitably lead to the loss of spatial structure information.Among the existing robust 2DPCA which can protect this structure,angle 2DPCA shows relatively outstanding anti-interference ability to noise.However,angle 2DPCA not only ignores the influence of mean data on robustness but also has low computational efficiency.More importantly,it cannot achieve convergence in theory,which leads to poor interpretability.Therefore,we proposed the feature extraction method based on robust optimal mean cosine angle 2DPCA.The method uses the R1-norm with rotational invariance as the distance metric and constructs the relationship between the variance of the projection data and input sample under the premise of considering the optimal mean,which not only enhances the ability to suppress noise interference but also improves the computational efficiency.Moreover,the method has good convergence and successfully protects the geometric structure information in the data.Experimental results illustrate that the proposed method effectively improves the description ability of robust 2DPCA for image main information.Fourth,the above mentioned robust 2DPCA method often needs more representation coefficients in the process of describing an image,which introduces some redundant information.Although the existing bilateral 2DPCA method can effectively reduce the use of expression coefficients,it usually has no real robustness to the complex noise information.To overcome this bottleneck,we proposed the feature extraction method based on adaptive sequential bilateral 2DPCA.In this method,the cutting l2,p-norm is used to sequentially compress the data in both the row and column directions,which not only ensures that the obtained projection direction has excellent robustness but also realizes the expectation of minimizing the reconstruction error to the greatest extent.In addition,the classifier based on nuclear norms is considered to complete the image recognition task,which further improves the recognition accuracy.On this basis,the proposed method reasonably inherits the valuable properties of PCA described before.A series of experimental results related to images show that the proposed method actively improves the recognition accuracy and clustering performance.