107 research outputs found
Iterative Reconstrained Low-rank Representation via Weighted Nonconvex Regularizer
OAPA Benefiting from the joint consideration of geometric structures and low-rank constraint, graph low-rank representation (GLRR) method has led to the state-of-the-art results in many applications. However, it faces the limitations that the structure of errors should be known a prior, the isolated construction of graph Laplacian matrix, and the over shrinkage of the leading rank components. To improve GLRR in these regards, this paper proposes a new LRR model, namely iterative reconstrained LRR via weighted nonconvex regularization (IRWNR), using three distinguished properties on the concerned representation matrix. The first characterizes various distributions of the errors into an adaptively learned weight factor for more flexibility of noise suppression. The second generates an accurate graph matrix from weighted observations for less afflicted by noisy features. The third employs a parameterized Rational function to reveal the importance of different rank components for better approximation to the intrinsic subspace structure. Following a deep exploration of automatic thresholding, parallel update, and partial SVD operation, we derive a computationally efficient low-rank representation algorithm using an iterative reconstrained framework and accelerated proximal gradient method. Comprehensive experiments are conducted on synthetic data, image clustering, and background subtraction to achieve several quantitative benchmarks as clustering accuracy, normalized mutual information, and execution time. Results demonstrate the robustness and efficiency of IRWNR compared with other state-of-the-art models
Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization
As a powerful statistical image modeling technique, sparse representation has
been successfully used in various image restoration applications. The success
of sparse representation owes to the development of l1-norm optimization
techniques, and the fact that natural images are intrinsically sparse in some
domain. The image restoration quality largely depends on whether the employed
sparse domain can represent well the underlying image. Considering that the
contents can vary significantly across different images or different patches in
a single image, we propose to learn various sets of bases from a pre-collected
dataset of example image patches, and then for a given patch to be processed,
one set of bases are adaptively selected to characterize the local sparse
domain. We further introduce two adaptive regularization terms into the sparse
representation framework. First, a set of autoregressive (AR) models are
learned from the dataset of example image patches. The best fitted AR models to
a given patch are adaptively selected to regularize the image local structures.
Second, the image non-local self-similarity is introduced as another
regularization term. In addition, the sparsity regularization parameter is
adaptively estimated for better image restoration performance. Extensive
experiments on image deblurring and super-resolution validate that by using
adaptive sparse domain selection and adaptive regularization, the proposed
method achieves much better results than many state-of-the-art algorithms in
terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI
A Deep-Unfolded Spatiotemporal RPCA Network For L+S Decomposition
Low-rank and sparse decomposition based methods find their use in many
applications involving background modeling such as clutter suppression and
object tracking. While Robust Principal Component Analysis (RPCA) has achieved
great success in performing this task, it can take hundreds of iterations to
converge and its performance decreases in the presence of different phenomena
such as occlusion, jitter and fast motion. The recently proposed deep unfolded
networks, on the other hand, have demonstrated better accuracy and improved
convergence over both their iterative equivalents as well as over other neural
network architectures. In this work, we propose a novel deep unfolded
spatiotemporal RPCA (DUST-RPCA) network, which explicitly takes advantage of
the spatial and temporal continuity in the low-rank component. Our experimental
results on the moving MNIST dataset indicate that DUST-RPCA gives better
accuracy when compared with the existing state of the art deep unfolded RPCA
networks
Hodge-Aware Contrastive Learning
Simplicial complexes prove effective in modeling data with multiway
dependencies, such as data defined along the edges of networks or within other
higher-order structures. Their spectrum can be decomposed into three
interpretable subspaces via the Hodge decomposition, resulting foundational in
numerous applications. We leverage this decomposition to develop a contrastive
self-supervised learning approach for processing simplicial data and generating
embeddings that encapsulate specific spectral information.Specifically, we
encode the pertinent data invariances through simplicial neural networks and
devise augmentations that yield positive contrastive examples with suitable
spectral properties for downstream tasks. Additionally, we reweight the
significance of negative examples in the contrastive loss, considering the
similarity of their Hodge components to the anchor. By encouraging a stronger
separation among less similar instances, we obtain an embedding space that
reflects the spectral properties of the data. The numerical results on two
standard edge flow classification tasks show a superior performance even when
compared to supervised learning techniques. Our findings underscore the
importance of adopting a spectral perspective for contrastive learning with
higher-order data.Comment: 4 pages, 2 figure
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