Dictionary Training for Sparse Representation as Generalization of K-Means Clustering

Sahoo, Sujit Kumar; Makur, Anamitra

doi:10.1109/lsp.2013.2258912

Cited by 111 publications

(55 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is necessary to develop an algorithm with lower computation cost by replacing each procedure with a high-speed procedure. For example, it has been reported that the computation cost of the KSVD algorithm used in SP-SIP-DIMS is high, and this problem can be solved by much faster versions such as those in [73] and [74]. These issues will be the subject of subsequent reports.…”

Section: Discussionmentioning

confidence: 99%

Adaptive Subspace-Based Inverse Projections via Division Into Multiple Sub-Problems for Missing Image Data Restoration

Ogawa

Haseyama

2016

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Abstract-This paper presents adaptive subspace-based inverse projections via division into multiple sub-problems (ASIP-DIMS) for missing image data restoration. In the proposed method, a target problem for estimating missing image data is divided into multiple sub-problems, and each sub-problem is iteratively solved with constraints of other known image data. By projection into a subspace model of image patches, the solution of each subproblem is calculated, where we call this procedure "subspacebased inverse projection" for simplicity. The proposed method can use higher-dimensional subspaces for finding unique solutions in each sub-problem, and successful restoration becomes feasible since a high level of image representation performance can be preserved. This is the biggest contribution of this paper. Furthermore, the proposed method generates several subspaces from known training examples and enables derivation of a new criterion in the above framework to adaptively select the optimal subspace for each target patch. In this way, the proposed method realizes missing image data restoration using ASIP-DIMS. Since our method can estimate any kind of missing image data, its potential in two image restoration tasks, image inpainting and super-resolution, based on several methods for multivariate analysis is also shown in this paper.

show abstract

Section: Discussionmentioning

confidence: 99%

Adaptive Subspace-Based Inverse Projections via Division Into Multiple Sub-Problems for Missing Image Data Restoration

Ogawa

Haseyama

2016

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

show abstract

“…Many sparse coding algorithms have been proposed [5]. Currently, the dictionary learning algorithms include method of optimal directions (MOD) [9], Kmeans singular value decomposition (KSVD) [10] or discriminative KSVD (DKSVD) [11], and sequential generalization of K-means (SGK) [12]. The main differences among them are in the second part, in which the dictionary is updated to reduce the representation error of stage 1.…”

Section: Proposed Methodsmentioning

confidence: 99%

“…(8), the SGK method [12] is used in the LRE-DLA to improve efficiency. The final classification of a test sample is based on its sparse code on the learned dictionary and the learned classifier.…”

Section: = Arg Minmentioning

confidence: 99%

Discriminative Dictionary Learning with Low-Rank Error Model for Robust Crater Recognition

Liu

Chen

Zhou

2015

IEICE Trans. Inf. & Syst.

View full text Add to dashboard Cite

SUMMARYRobust crater recognition is a research focus on deep space exploration mission, and sparse representation methods can achieve desirable robustness and accuracy. Due to destruction and noise incurred by complex topography and varied illumination in planetary images, a robust crater recognition approach is proposed based on dictionary learning with a low-rank error correction model in a sparse representation framework. In this approach, all the training images are learned as a compact and discriminative dictionary. A low-rank error correction term is introduced into the dictionary learning to deal with gross error and corruption. Experimental results on crater images show that the proposed method achieves competitive performance in both recognition accuracy and efficiency.

show abstract

“…The square of the Frobenius nonn was used in [1] to derive a sequential dic tionary update stage. Other examples of sequential dictionary learning algorithms can be found in [12] [13]. The sparsity constraint used in the sparse coding stage is the pillar of any dictionary learning algorithm.…”

Section: Muhammad Hanifmentioning

confidence: 99%

A sequential dictionary learning algorithm with enforced sparsity

Seghouane

Hanif

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

Dictionary learning algorithms have received widespread ac ceptance when it comes to data analysis and signal represen tations problems. These algorithms alternate between two stages: the sparse coding stage and dictionary update stage. In all existing dictionary learning algorithms the use of spar sity has been limited to the sparse coding stage while pre senting differences in the dictionary update stage which can be achieved sequentially or in parallel. The singular value decomposition (SVD) has been successfully used for sequen tial dictionary update. In this paper we propose a dictionary learning algorithm that include a sparsity constraint also in the dictionary update stage. The cost function used to include sparsity in the dictionary update stage is derived using the link between SVD and rank one matrix approximation. The effec tiveness of the proposed dictionary learning method is tested on synthetic data and an image processing application. The results reveal that including a sparsity constraint in the dictio nary update stage is not a bad idea.Index Terms-Dictionary learning, sparsity, SVD, se quential update, penalized rank one approximation. 1. IN TRODUCTION Dictionary learning methods have been successfully used in a number of signal and image processing applications among them image denoising [1][2], face recognition [3], compres sion [4] and fMRI data analysis [S][6][7]. These methods seek to uncover a linear multivariable latent structure in the observed data by imposing the reasonable constraint that the estimates of the observed variables are sparse linear func tions of some unknown regressors (atoms of the dictionary). The other particularity of these methods is that this set of regressors or the dictionary is also tuned iteratively to find the optimal linear multivariable latent model. Dictionary learning algorithms consist of two stages: a sparse coding stage and a dictionary update stage. In the first stage the dictionary is kept constant and the sparsity assumption is used to produce sparse linear approximations of the ob served data. In the second stage, the coefficients of the linear combination are kept constant and the dictionary is updated to minimize a certain cost function. The dictionary learning methods iterate between these two stages until convergence. The perfonnance of these methods strongly depend on the dictionary update stage since most of these methods share a similar sparse coding stage. Dictionary learning through the dictionary update stage can also be made sequential or paral lel. For a specific strategy or goal (characterized by the cost function used to update the dictionary), the parallel approach will generally require a lower computational cost than the sequential approach that uses the same strategy. While the parallel update approach may be preferred for its advantage in computational complexity, the sequential approach generally offers better results because it generates finer tuned dictionary atoms. Probabilistic and non-probabilistic approaches have been adop...

show abstract

Dictionary Training for Sparse Representation as Generalization of K-Means Clustering

Cited by 111 publications

References 5 publications

Adaptive Subspace-Based Inverse Projections via Division Into Multiple Sub-Problems for Missing Image Data Restoration

Adaptive Subspace-Based Inverse Projections via Division Into Multiple Sub-Problems for Missing Image Data Restoration

Discriminative Dictionary Learning with Low-Rank Error Model for Robust Crater Recognition

A sequential dictionary learning algorithm with enforced sparsity

Contact Info

Product

Resources

About