Abstract-We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained in the "shortest possible path", essentially solving the traveling salesman problem. The obtained ordering applied to the corrupted image, implies a permutation of the image pixels to what should be a regular signal. This enables us to obtain good recovery of the clean image by applying relatively simple one-dimensional (1D) smoothing operations (such as filtering or interpolation) to the reordered set of pixels. We explore the use of the proposed approach to image denoising and inpainting, and show promising results in both cases.
Abstract-In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical tree, which is assumed to capture the geometry and structure of the input data. It is applied to the data using a modified version of the common 1D wavelet filtering and decimation scheme, which can employ different wavelet filters. In each level of this wavelet decomposition scheme, a permutation derived from the tree is applied to the approximation coefficients, before they are filtered. We propose a tree construction method that results in an efficient representation of the input function in the transform domain. We show that the proposed transform is more efficient than both the one-dimensional (1D) and two-dimensional (2D) separable wavelet transforms in representing images. We also explore the application of the proposed transform to image denoising, and show that combined with a subimage averaging scheme, it achieves denoising results which are similar to those obtained with the K-SVD algorithm.
Patients with unipolar depressive disorder and in the depressive phase of bipolar disorder often manifest psychological distress and cognitive deficits, notably in executive control. We used computerized cognitive training in an attempt to reduce psychological affliction, improve everyday coping, and cognitive function. We asked one group of patients (intervention group) to engage in cognitive training three times a week, for 20 min each time, for eight consecutive weeks. A second group of patients (control group) received standard care only. Before the onset of training we administered to all patients self-report questionnaires of mood, mental and psychological health, and everyday coping. We also assessed executive control using a broad computerized neurocognitive battery of tests which yielded, among others, scores in Working Memory, Shifting, Inhibition, Visuomotor Vigilance, Divided Attention, Memory Span, and a Global Executive Function score. All questionnaires and tests were re-administered to the patients who adhered to the study at the end of training. When we compared the groups (between-group comparisons) on the amount of change that had taken place from baseline to post-training, we found significantly reduced depression level for the intervention group. This group also displayed significant improvements in Shifting, Divided Attention, and in the Global executive control score. Further exploration of the data showed that the cognitive improvement did not predict the improvements in mood. Single-group data (within-group comparisons) show that patients in the intervention group were reporting fewer cognitive failures, fewer dysexecutive incidents, and less difficulty in everyday coping. This group had also improved significantly on the six executive control tests and on the Global executive control score. By contrast, the control group improved only on the reports of cognitive failure and on working memory.
Learning analytics are often formatted as visualisations developed from traced data collected as students study in online learning environments. Optimal analytics inform and motivate students' decisions about adaptations that improve their learning. We observe that designs for learning often neglect theories and empirical findings in learning science that explain how students learn. We present six learning analytics that reflect what is known in six areas (we call them cases) of theory and research findings in the learning sciences: setting goals and monitoring progress, distributed practice, retrieval practice, prior knowledge for reading, comparative evaluation of writing, and collaborative learning. Our designs demonstrate learning analytics can be grounded in research on self-regulated learning and self-determination. We propose designs for learning analytics in general should guide students toward more effective self-regulated learning and promote motivation through perceptions of autonomy, competence, and relatedness.
Abstract-In our previous work [1] we have introduced a redundant tree-based wavelet transform (RTBWT), originally designed to represent functions defined on high dimensional data clouds and graphs. We have further shown that RTBWT can be used as a highly effective image-adaptive redundant transform that operates on an image using orderings of its overlapped patches. The resulting transform is robust to corruptions in the image, and thus able to efficiently represent the unknown target image even when it is calculated from its corrupted version.In this work we utilize this redundant transform as a powerful sparsity-promoting regularizer in inverse problems in image processing. We show that the image representation obtained with this transform is a frame expansion, and derive the analysis and synthesis operators associated with it. We explore the use of this frame operators to image denoising and deblurring, and demonstrate in both these cases state-of-the-art results.
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