Learned dictionaries for sparse image representation: properties and results (original) (raw)
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Supervised Dictionary Learning and Sparse Representation-A Review
Dictionary learning and sparse representation (DLSR) is a recent and successful mathematical model for data representation that achieves state-ofthe-art performance in various fields such as pattern recognition, machine learning, computer vision, and medical imaging. The original formulation for DLSR is based on the minimization of the reconstruction error between the original signal and its sparse representation in the space of the learned dictionary. Although this formulation is optimal for solving problems such as denoising, inpainting, and coding, it may not lead to optimal solution in classification tasks, where the ultimate goal is to make the learned dictio- * Corresponding author Email addresses: mehrdad.gangeh@utoronto.ca (Mehrdad J. Gangeh), afarahat@pami.uwaterloo.ca (Ahmed K. Farahat), aghodsib@uwaterloo.ca (Ali Ghodsi), mkamel@pami.uwaterloo.ca (Mohamed S. Kamel)
Efficient Dictionary Learning with Sparseness-Enforcing Projections
International Journal of Computer Vision, 2015
Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is enforced to be explicitly sparse with respect to a smooth, normalized sparseness measure. This involves the computation of Euclidean projections onto level sets of the sparseness measure. While previous algorithms for this optimization problem had at least quasi-linear time complexity, here the first algorithm with linear time complexity and constant space complexity is proposed. The key for this is the mathematically rigorous derivation of a characterization of the projection's result based on a soft-shrinkage function. This theory is applied in an original algorithm called Easy Dictionary Learning (EZDL), which learns dictionaries with a simple and fast-to-compute Hebbian-like learning rule. The new algorithm is efficient, expressive and particularly simple to implement. It is demonstrated that despite its simplicity, the proposed learning algorithm is able to generate a rich variety of dictionaries, in particular a topographic organization of atoms or separable atoms. Further, the dictionaries are as expressive as those of benchmark learning algorithms in terms of the reproduction quality on entire images, and result in an equivalent denoising performance. EZDL learns approximately 30 % faster than the already very efficient Online Dictionary Learning algorithm, and is Communicated by Julien Mairal, Francis Bach, Michael Elad.
An Efficient Dictionary Learning Algorithm for Sparse Representation
2010 Chinese Conference on Pattern Recognition (CCPR), 2010
Sparse and redundant representation of data assumes an ability to describe signals as linear combinations of a few atoms from a dictionary. If the model of the signal is unknown, the dictionary can be learned from a set of training signals. Like the K-SVD, many of the practical dictionary learning algorithms are composed of two main parts: sparse-coding and dictionary-update. This paper first proposes a Stagewise least angle regression (St-LARS) method for performing the sparse-coding operation. The St-LARS applies a hard-thresholding strategy into the original least angle regression (LARS) algorithm, which enables it to select many atoms at each iteration and thus results in fast solutions while still provides good results. Then, a dictionary update method named approximated singular value decomposition (ASVD) is used on the dictionary update stage. It is a quick approximation of the exact SVD computation and can reduce the complexity of it. Experiments on both synthetic data and 3-D image denoising demonstrate the advantages of the proposed algorithm over other dictionary learning methods not only in terms of better trained dictionary but also in terms of computation time.
An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation
In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data.
Dictionary Learning for Sparse Representation: A Novel Approach
IEEE Signal Processing Letters, 2000
A dictionary learning problem is a matrix factorization in which the goal is to factorize a training data matrix, , as the product of a dictionary, , and a sparse coefficient matrix, , as follows, . Current dictionary learning algorithms minimize the representation error subject to a constraint on (usually having unit column-norms) and sparseness of . The resulting problem is not convex with respect to the pair . In this letter, we derive a first order series expansion formula for the factorization, . The resulting objective function is jointly convex with respect to and . We simply solve the resulting problem using alternating minimization and apply some of the previously suggested algorithms onto our new problem. Simulation results on recovery of a known dictionary and dictionary learning for natural image patches show that our new problem considerably improves performance with a little additional computational load.
Digital Signal Processing, 2007
The use of overcomplete dictionaries, or frames, for sparse signal representation has been given considerable attention in recent years. The major challenges are good algorithms for sparse approximations, i.e., vector selection algorithms, and good methods for choosing or designing dictionaries/frames. This work is concerned with the latter. We present a family of iterative least squares based dictionary learning algorithms (ILS-DLA), including algorithms for design of signal dependent block based dictionaries and overlapping dictionaries, as generalizations of transforms and filter banks, respectively. In addition different constraints can be included in the ILS-DLA, thus we present different constrained design algorithms. Experiments show that ILS-DLA is capable of reconstructing (most of) the generating dictionary vectors from a sparsely generated data set, with and without noise. The dictionaries are shown to be useful in applications like signal representation and compression where experiments demonstrate that our ILS-DLA dictionaries substantially improve compression results compared to traditional signal expansions such as transforms and filter banks/wavelets.
Dictionary Learning Algorithms for Sparse Representation
Neural Computation, 2003
Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave (CSC) negative log priors. Such priors are appropriate for obtaining sparse representations of environmental signals within an appropriately chosen (environmentally matched) dictionary. The elements of the dictionary can be interpreted as concepts, features, or words capable of succinct expression of events encountered in the environment (the source of the measured signals). This is a generalization of vector quantization in that one is interested in a description involving a few dictionary entries (the proverbial "25 words or less"), but not necessarily as succinct as one entry. To learn an environmentally adapted dictionary capable of concise expression of signals generated by the environment, we develop algorithms that iterate between a representative set of sparse representations found by variants of FOCUSS and an update of the dictionary using these sparse representations.
Dictionary Learning Based Applications in Image Processing using Convex Optimisation
2016
In this term paper, sparse based representation of images has been exploited for various applications. Sparse and redundant representation is based on the assumptions that the signals can be described as a linear combination of a few atoms from the pre-defined dictionary. Dictionary atoms is either selected using k-SVD algorithm or taken as standard DCT atoms. Dictionary atoms can lso be set by randomly sampling patches from the image. Different applications of sparse based representation have been presented. Image Inpainting, classification and Image denoising applications based on sparse representation are presented. Sparse representation based applications have very similar performances with the state of the art methods. Keywords—Sparse, OMP, K-SVD, DCT.
Shift-invariant sparse representation of images using learned dictionaries
2008
Abstract Sparse approximations that are evaluated using over complete learned dictionaries are useful in many image processing applications such as compression, denoising and feature extraction. Incorporating shift invariance into sparse representation of images can improve sparsity while providing a good approximation. The K-SVD algorithm adapts the dictionary based on a set of training examples, without shift invariance constraints.
Sparse coding and dictionary learning for image understanding
Procedings of the British Machine Vision Conference 2010, 2010
Sparse coding-that is, modeling data vectors as sparse linear combinations of dictionary elements-is widely used in machine learning, neuroscience, signal processing, and statistics. This talk addresses the problem of learning the dictionary, adapting it to specific data and image understanding tasks. In particular, I will present a fast on-line approach to unsupervised dictionary learning and more generally sparse matrix factorization, and demonstrate its applications in image restoration tasks such as denoising, demosaicking, and inpainting. I will also present a general formulation of supervised dictionary learning adapted to tasks such as classification and regression. We have developed an efficient algorithm for solving the corresponding optimization problem, and I will demonstrate its application to handwritten digit classification, image deblurring and digital zooming, inverse half toning, and the detection of fake artworks.