Art Modeling Liliana Model
In digital images, blockiness, known as a common defect in pictures, is one of the major issues to severely hamper image capture quality. This problem is generally caused by the noise that remains even after standard pre-processing steps of image denoising. In this study, we aim to alleviate this noise defect by rebuilding better image blocks using the L1 distance. To this end, first, we propose a block-based texture model with a new filtering function. Next, we develop an iterative L1 image reconstruction model using graph regularization, where the consistency of neighboring blocks is guaranteed by a suitable decomposition (tracking of blocks). The proposed method combines defocusing with robust smoothing and adaptive reconstruction. First, we solve the L1 reconstruction problem by a multi-block gradient descent algorithm. Second, a nonlocal regularization is inserted to improve the reconstruction. Finally, the stitching property is guaranteed through a sequential tree construction of blocks. We prove that the above steps are algebraically equivalent to the minimization of a functional with a graph Laplacian that becomes an L1 energy with an empirical measurement function. Our experimental results show that the proposed algorithm produces cleaner and sharper reconstructions for various noisy images with an accuracy of 80% to 98%.
Manifold learning has gained a lot of stimulus in the last few years due to the rapid growth of big data in diverse fields. One of the most appealing applications of manifold learning is to address the distributional shift of data. For this purpose, we have designed a multi-view probability model that yields an L2 distance based on a model of functional data on the manifold. To our knowledge, it is the first study to provide a general nonlinear manifold learning model based on the number of learning data and to allow automatic tuning of parameters under noisy conditions. Our proposed model can also be extended to a generative model by including not only the training data but also the hidden variables to represent the function generating the data. Moreover, the multivariate extension of the proposed framework can be used to extend our method to integrate variables on a manifold with missing values. In addition, we proposed a predictive discrepancy that integrates a surrogate model that takes into account the probability that the events taking place at neighboring points will be similar. It is shown that our method provides a more accurate estimate of the probability distribution than the standard distributions such as Gaussian, exponential, and uniform distributions.
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