Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Binary sparse nonnegative matrix factorization
IEEE Transactions on Circuits and Systems for Video Technology
Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries
IEEE Transactions on Image Processing
Sparse Representation for Color Image Restoration
IEEE Transactions on Image Processing
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Sparse modelling involves constructing a succinct representation of initial data as a linear combination of a few typical atoms of a dictionary. This paper deals with the use of sparse representations to introduce new nonlinear operators which efficiently approximate the dilation/erosion. Non-negative matrix factorization (NMF) is a dimensional reduction (i.e., dictionary learning) paradigm particularly adapted to the nature of morphological processing. Sparse NMF representations are studied to introduce pseudo-morphological binary dilations/erosions. The basic idea consists in processing exclusively the image dictionary and then, the result of processing each image is approximated by multiplying the processed dictionary by the coefficient weights of the current image. These operators are then extended to grey-level images by means of the level-set decomposition. The performance of the present method is illustrated using families of binary shapes and face images.