Image interpolation via regularized local linear regression

In this paper, we present an efficient image interpolation scheme by using regularized local linear regression (RLLR). On one hand, we introduce a robust estimator of local image structure based on moving least squares, which can efficiently handle the statistical outliers compared with ordinary least squares based methods. On the other hand, motivated by recent progress on manifold based semi-supervise learning, the intrinsic manifold structure is explicitly considered by making use of both measured and unmeasured data points. In particular, the geometric structure of the marginal probability distribution induced by unmeasured samples is incorporated as an additional locality preserving constraint. The optimal model parameters can be obtained with a closed-form solution by solving a convex optimization problem. Experimental results demonstrate that our method outperform the existing methods in both objective and subjective visual quality over a wide range of test images. ? 2010 IEEE.EI

High Quality Image Interpolation via Local Autoregressive and Nonlocal 3-D Sparse Regularization

In this paper, we propose a novel image interpolation algorithm, which is formulated via combining both the local autoregressive (AR) model and the nonlocal adaptive 3-D sparse model as regularized constraints under the regularization framework. Estimating the high-resolution image by the local AR regularization is different from these conventional AR models, which weighted calculates the interpolation coefficients without considering the rough structural similarity between the low-resolution (LR) and high-resolution (HR) images. Then the nonlocal adaptive 3-D sparse model is formulated to regularize the interpolated HR image, which provides a way to modify these pixels with the problem of numerical stability caused by AR model. In addition, a new Split-Bregman based iterative algorithm is developed to solve the above optimization problem iteratively. Experiment results demonstrate that the proposed algorithm achieves significant performance improvements over the traditional algorithms in terms of both objective quality and visual perceptionComment: 4 pages, 5 figures, 2 tables, to be published at IEEE Visual Communications and Image Processing (VCIP) 201

A study of the classification of low-dimensional data with supervised manifold learning

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of supervised manifold learning for classification. We consider nonlinear dimensionality reduction algorithms that yield linearly separable embeddings of training data and present generalization bounds for this type of algorithms. A necessary condition for satisfactory generalization performance is that the embedding allow the construction of a sufficiently regular interpolation function in relation with the separation margin of the embedding. We show that for supervised embeddings satisfying this condition, the classification error decays at an exponential rate with the number of training samples. Finally, we examine the separability of supervised nonlinear embeddings that aim to preserve the low-dimensional geometric structure of data based on graph representations. The proposed analysis is supported by experiments on several real data sets