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Compressed sensing is the ability to retrieve a sparse vector from a set of linear measurements. The task gets more difficult when the sensing process is not perfectly known. We address such a problem in the case where the sensors have been permuted, i.e., the order of the measurements is unknown. We propose a branch-and-bound algorithm that converges to the solution. The experimental study shows...
The traditional compression system only considers the statistical redundancy of images. Recent compression works exploit the visual redundancy of images to further improve the coding efficiency. However, the existing works only provide suboptimal visual redundancy removal schemes. In this paper, we propose an efficient image compression scheme based on the selection and reconstruction of the visual...
This work proposes a novel design method of a two-dimensional (2-D) Non-Separable Oversampled Lapped Transform (NSOLT) for a given image by introducing a typical two stage procedure of dictionary learning. NSOLT is a lattice-structure-based transform and yields a redundant dictionary of which atoms satisfy the non-separable, symmetric, real-valued, overlapping and compact-support property. In addition,...
We consider the problem where a large known library of L alternatives is available and we wish to maximize the detection power in a worst case scenario. The considered minimax detection approach relies on a GLR test allied to a sparsity constraint. This approach conditions the optimization of the target subspaces, in number r ≪ L. While the exact solution of the minimax optimization problem can be...
Sparse dictionary learning has attracted enormous interest in image processing and data representation in recent years. To improve the performance of dictionary learning, we propose an efficient block-structured incoherent K-SVD algorithm for the sparse representation of signals. Without relying on any prior knowledge of the group structure for the input data, we develop a two-stage agglomerative...
Several approaches used for inpainting of images take advantage of sparse representations. Some of these seek to learn a dictionary that will adapt the sparse representation to the available data. A further refinement is to adapt the learning process to the task itself. In this paper, we formulate a task-driven approach to inpainting as an optimization problem, and derive an algorithm for solving...
This paper presents a new framework for facial motion modeling with applications to facial expression recognition. First, we design sparse localized facial motion dictionaries from dense motion flow data of facial expression image sequences. Regularization based on spatial localized support map in addition to the sparsity constraints enables spatially localized dictionary learning. Proposed localized...
Sparse representations of images in well-designed dictionaries can be used for effective classification. Meanwhile, training data available in most realistic settings are likely to be exposed to geometric transformations, which poses a challenge for the design of good dictionaries. In this work, we study the problem of learning class-representative dictionaries from geometrically transformed image...
Video representation is an important and challenging task in the computer vision community. In this paper, we assume that image frames of a moving scene can be modeled as a Markov random process. We propose a sparse coding framework, named adaptive video dictionary learning (AVDL), to model a video adaptively. The developed framework is able to capture the dynamics of a moving scene by exploring both...
In this paper, we consider learning dictionary models over a network of agents, where each agent is only in charge of a portion of the dictionary elements. This formulation is relevant in big data scenarios where multiple large dictionary models may be spread over different spatial locations and it is not feasible to aggregate all dictionaries in one location due to communication and privacy considerations...
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard and then propose an efficient dictionary learning scheme to solve several practical formulations of this problem. Unlike many existing algorithms in the literature, such as K-SVD, our proposed dictionary learning scheme is theoretically guaranteed to converge to the set of...
We propose a novel approach to performing change-detection based on sparse representations and dictionary learning. We operate on observations that are finite support signals, which in stationary conditions lie within a union of low dimensional subspaces. We model changes as perturbations of these subspaces and provide an online and sequential monitoring solution to detect them. This approach allows...
The current sparse representation framework is to decouple it as two subproblems, i.e., alternate sparse coding and dictionary learning using different optimizers, treating elements in bases and codes separately. In this paper, we treat elements both in bases and codes ho-mogenously. The original optimization is directly decoupled as several blockwise alternate subproblems rather than above two. Hence,...
In current color image super-resolution methods, superresolution based on sparse representation achieves state-of-the-art performance. However, the exploited sparse representation models deal with the color images as independent channel planes. Consequently, these approaches process the color pixels as scalar quantity, lacking of accuracy in describing inter-relationship among color channels. In this...
In this paper we present an efficient initialization strategy that improves the performance of overcomplete dictionary learning algorithms. The procedure exploits incoherent structures that can be manipulated and adapted to a given dataset relatively fast. The algorithm involves an iterative adaptation of the dictionary to the dataset with pruning of the less used atoms and constructions of new atoms...
Analysis sparsity and the accompanying analysis operator learning problem provide an important framework for signal modeling. Very recently, sparsifying transform learning has been put forward as an effective and new formulation for the analysis operator learning problem. In this study, we develop a new sparsifying transform learning algorithm by using the uniform normalized tight frame constraint...
Overcomplete representations and dictionary learning algorithms are attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete dictionaries. Despite a recurrent need to rely on a distance for learning or assessing multivariate overcomplete dictionaries, no metrics in their underlying spaces have yet been proposed...
The kernel least-mean-square (KLMS) algorithm is an appealing tool for online identification of nonlinear systems due to its simplicity and robustness. In addition to choosing a reproducing kernel and setting filter parameters, designing a KLMS adaptive filter requires to select a so-called dictionary in order to get a finite-order model. This dictionary has a significant impact on performance, and...
This paper presents a novel feature representation called sparse cepstral codes for instrument identification. We first motivate the approach by discussing why cepstrum is suitable for instrument identification. Then we propose the use of sparse coding and power normalization to derive compact codes that better represent the information of the cepstrum. Our evaluation on both uni-source and multi-source...
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