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SPARSE REPRESENTATION OF IMAGES WITH HYBRID LINEAR MODELS



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SPARSE REPRESENTATION OF IMAGES WITH HYBRID LINEAR MODELS Kun Huang Allen Y Yang Yi Ma Coordinated Science Laboratory University of Illinois Urbana IL 61801 Email kunhuang yangyang yima uiuc edu ing data into respective models was usually resolved via an incremental scheme that iterates between segmentation We propose a mixture of multiple linear models also known and estimation e g the expectation maximization EM as hybrid linear model for a sparse representation of an immethod It has only recently been discovered that a nonage This is a generalization of the conventional KarhunenLoeve transform KLT or principal component analysis PCA iterative and global solution called generalized principal component analysis GPCA 24 13 exists for the segWe provide an algebraic algorithm based on generalized mentation and estimation of hybrid linear models The idea principal component analysis GPCA that gives a global that image segmentation may improve image compression and non iterative solution to the identification of a hybrid is not new However we believe that GPCA is a method linear model for any given image We demonstrate the efthat can seamlessly combine these two key components in ficiency of the proposed hybrid linear model by experiments image processing It offers the new capability to represent and comparison with other transforms such as the KLT DCT different image regions with different colors and textures by and wavelet transforms Such an efficient representation can different linear models with different linear bases be very useful for later stages of image processing espeRelation to prior work There is a vast amount of litercially in applications such as image segmentation and image ature on finding adaptive bases or transforms for signals compression Adaptive wavelet transforms and adapted wavelet packets 1 INTRODUCTION have been extensively studied 4 20 15 6 18 The idea is In image processing one often seeks a more efficient repto search for an optimal



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