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In a broad range of computer vision applications, the purpose of Low-rankmatrix approximation (LRMA) models is to recover the underlying low-rank matrixfrom its degraded observation. The latest LRMA methods - Robust PrincipalComponent Analysis (RPCA) resort to using the nuclear norm minimization (NNM)as a convex relaxation of the non-convex rank minimization. However, NNM tendsto over-shrink the rank components and treats the different rank componentsequally, limiting its flexibility in practical applications. We use a moreflexible model, namely the Weighted Schatten p-Norm Minimization (WSNM), togeneralize the NNM to the Schatten p-norm minimization with weights assigned todifferent singular values. The proposed WSNM not only gives a betterapproximation to the original low-rank assumption but also considers theimportance of different rank components. In this paper, a comparison of thelow-rank recovery performance of two LRMA algorithms- RPCA and WSNM is broughtout on occluded human facial images. The analysis is performed on facial imagesfrom the Yale database and over own database , where different facialexpressions, spectacles, varying illumination account for the facialocclusions. The paper also discusses the prominent trends observed from theexperimental results performed through the application of these algorithms. Aslow-rank images sometimes might fail to capture the details of a faceadequately, we further propose a novel method to use the image-histogram of thesparse images thus obtained to identify the individual in any given image.Extensive experimental results show, both qualitatively and quantitatively,that WSNM surpasses RPCA in its performance more effectively by removing facialocclusions, thus giving recovered low-rank images of higher PSNR and SSIM.

Performance analysis of weighted low rank model with sparse image histograms for face recognition under lowlevel illumination and occlusion