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Register a new userLow-Rank Modeling and Its Applications in Image Analysis
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Xiaowei Zhou
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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Low-rank modeling generally refers to a class of methods that solve problems by representing variables of interest as low-rank matrices. It has achieved great success in various fields including computer vision, data mining, signal processing and bioinformatics. Recently, much progress has been made in theories, algorithms and applications of low-rank modeling, such as exact low-rank matrix recovery via convex programming and matrix completion applied to collaborative filtering. These advances have brought more and more attentions to this topic. In this paper, we review the recent advance of low-rank modeling, the state-of-the-art algorithms, and related applications in image analysis. We first give an overview to the concept of low-rank modeling and challenging problems in this area. Then, we summarize the models and algorithms for low-rank matrix recovery and illustrate their advantages and limitations with numerical experiments. Next, we introduce a few applications of low-rank modeling in the context of image analysis. Finally, we conclude this paper with some discussions.
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Finding compact representation of videos is an essential component in almost every problem related to video processing or understanding. In this paper, we propose a generative model to learn compact latent codes that can efficiently represent and reconstruct a video sequence from its missing or under-sampled measurements. We use a generative network that is trained to map a compact code into an image. We first demonstrate that if a video sequence belongs to the range of the pretrained generative network, then we can recover it by estimating the underlying compact latent codes. Then we demonstrate that even if the video sequence does not belong to the range of a pretrained network, we can still recover the true video sequence by jointly updating the latent codes and the weights of the generative network. To avoid overfitting in our model, we regularize the recovery problem by imposing low-rank and similarity constraints on the latent codes of the neighboring frames in the video sequence. We use our methods to recover a variety of videos from compressive measurements at different compression rates. We also demonstrate that we can generate missing frames in a video sequence by interpolating the latent codes of the observed frames in the low-dimensional space.
We propose a new method for creating computationally efficient convolutional neural networks (CNNs) by using low-rank representations of convolutional filters. Rather than approximating filters in previously-trained networks with more efficie
Recent works on adaptive sparse and on low-rank signal modeling have demonstrated their usefulness in various image / video processing applications. Patch-based methods exploit local patch sparsity, whereas other works apply low-rankness of grouped patches to exploit image non-local structures. However, using either approach alone usually limits performance in image reconstruction or recovery applications. In this work, we propose a simultaneous sparsity and low-rank model, dubbed STROLLR, to better represent natural images. In order to fully utilize both the local and non-local image properties, we develop an image restoration framework using a transform learning scheme with joint low-rank regularization. The approach owes some of its computational efficiency and good performance to the use of transform learning for adaptive sparse representation rather than the popular synthesis dictionary learning algorithms, which involve approximation of NP-hard sparse coding and expensive learning steps. We demonstrate the proposed framework in various applications to image denoising, inpainting, and compressed sensing based magnetic resonance imaging. Results show promising performance compared to state-of-the-art competing methods.
We propose LSDAT, an image-agnostic decision-based black-box attack that exploits low-rank and sparse decomposition (LSD) to dramatically reduce the number of queries and achieve superior fooling rates compared to the state-of-the-art decision-based methods under given imperceptibility constraints. LSDAT crafts perturbations in the low-dimensional subspace formed by the sparse component of the input sample and that of an adversarial sample to obtain query-efficiency. The specific perturbation of interest is obtained by traversing the path between the input and adversarial sparse components. It is set forth that the proposed sparse perturbation is the most aligned sparse perturbation with the shortest path from the input sample to the decision boundary for some initial adversarial sample (the best sparse approximation of shortest path, likely to fool the model). Theoretical analyses are provided to justify the functionality of LSDAT. Unlike other dimensionality reduction based techniques aimed at improving query efficiency (e.g, ones based on FFT), LSD works directly in the image pixel domain to guarantee that non-$ell_2$ constraints, such as sparsity, are satisfied. LSD offers better control over the number of queries and provides computational efficiency as it performs sparse decomposition of the input and adversarial images only once to generate all queries. We demonstrate $ell_0$, $ell_2$ and $ell_infty$ bounded attacks with LSDAT to evince its efficiency compared to baseline decision-based attacks in diverse low-query budget scenarios as outlined in the experiments.
Visual saliency modeling for images and videos is treated as two independent tasks in recent computer vision literature. While image saliency modeling is a well-studied problem and progress on benchmarks like SALICON and MIT300 is slowing, video saliency models have shown rapid gains on the recent DHF1K benchmark. Here, we take a step back and ask: Can image and video saliency modeling be approached via a unified model, with mutual benefit? We identify different sources of domain shift between image and video saliency data and between different video saliency datasets as a key challenge for effective joint modelling. To address this we propose four novel domain adaptation techniques - Domain-Adaptive Priors, Domain-Adaptive Fusion, Domain-Adaptive Smoothing and Bypass-RNN - in addition to an improved formulation of learned Gaussian priors. We integrate these techniques into a simple and lightweight encoder-RNN-decoder-style network, UNISAL, and train it jointly with image and video saliency data. We evaluate our method on the video saliency datasets DHF1K, Hollywood-2 and UCF-Sports, and the image saliency datasets SALICON and MIT300. With one set of parameters, UNISAL achieves state-of-the-art performance on all video saliency datasets and is on par with the state-of-the-art for image saliency datasets, despite faster runtime and a 5 to 20-fold smaller model size compared to all competing deep methods. We provide retrospective analyses and ablation studies which confirm the importance of the domain shift modeling. The code is available at https://github.com/rdroste/unisal
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