Image Superresolution Reconstruction via Granular Computing Clustering

The problem of generating a superresolution (SR) image from a single low-resolution (LR) input image is addressed via granular computing clustering in the paper. Firstly, and the training images are regarded as SR image and partitioned into some SR patches, which are resized into LS patches, the training set is composed of the SR patches and the corresponding LR patches. Secondly, the granular computing (GrC) clustering is proposed by the hypersphere representation of granule and the fuzzy inclusion measure compounded by the operation between two granules. Thirdly, the granule set (GS) including hypersphere granules with different granularities is induced by GrC and used to form the relation between the LR image and the SR image by lasso. Experimental results showed that GrC achieved the least root mean square errors between the reconstructed SR image and the original image compared with bicubic interpolation, sparse representation, and NNLasso

Piecewise-linear approximation of nonlinear models based on interval numbers (INs)

Linear models are ususally preferable due to their simplicity. However, nonlinear models often emerge in practice. A popular approach for dealing with nonlinearities is using a piecewise-linear approximation. In such context, inspired from both Fuzzy Inference Systems (FISs) of TSK type and Self-Organizing Maps (SOMs), this work introduces enhancements based on Interval Numbers and, ultimately, on lattice theory. Advantages include a capacity to deal with granular inputs, introduction of tunable nonlinearities, representation of all-order statistics, and induction of descriptive decision-making knowledge (rules) from the training data. Preliminary computational experiments here demonstrate a good capacity for generalization; furthermore, only a few rules are induced