arXiv subjects

Karthikeyan Natesan Ramamurthy

Publications and source records attributed to Karthikeyan Natesan Ramamurthy.

76 records · Page 5Linked to original sources

arXiv2013

Learning Stable Multilevel Dictionaries for Sparse Representations

Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient, robust and provably good dictionary learning algorithms. Algorithmic stability and generalization are desirable characteristics for dictionary learning algorithms that aim to build global dictionaries which can efficiently model any test data similar to the training samples. In this paper, we propose an algorithm to learn dictionaries for sparse representations from large scale data, and prove that the proposed learning algorithm is stable and generalizable asymptotically. The algorithm employs a 1-D subspace clustering procedure, the K-hyperline clustering, in order to learn a hierarchical dictionary with multiple levels. We also propose an information-theoretic scheme to estimate the number of atoms needed in each level of learning and develop an ensemble approach to learn robust dictionaries. Using the proposed dictionaries, the sparse code for novel test data can be computed using a low-complexity pursuit procedure. We demonstrate the stability and generalization characteristics of the proposed algorithm using simulations. We also evaluate the utility of the multilevel dictionaries in compressed recovery and subspace learning applications.

cs.CV↗

arXiv2013

Recovering Non-negative and Combined Sparse Representations

The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we develop the paradigm of combined sparse representations, where only a part of the coefficient vector is constrained to be non-negative, and the rest is unconstrained (general). We analyze the recovery of the unique, sparsest solution, for combined representations, under three different cases of coefficient support knowledge: (a) the non-zero supports of non-negative and general coefficients are known, (b) the non-zero support of general coefficients alone is known, and (c) both the non-zero supports are unknown. For case (c), we propose the combined orthogonal matching pursuit algorithm for coefficient recovery and derive the deterministic sparsity threshold under which recovery of the unique, sparsest coefficient vector is possible. We quantify the order complexity of the algorithms, and examine their performance in exact and approximate recovery of coefficients under various conditions of noise. Furthermore, we also obtain their empirical phase transition characteristics. We show that the basis pursuit algorithm, with partial non-negative constraints, and the proposed greedy algorithm perform better in recovering the unique sparse representation when compared to their unconstrained counterparts. Finally, we demonstrate the utility of the proposed methods in recovering images corrupted by saturation noise.

math.NA↗

arXiv2013

Kernel Sparse Models for Automated Tumor Segmentation

In this paper, we propose sparse coding-based approaches for segmentation of tumor regions from MR images. Sparse coding with data-adapted dictionaries has been successfully employed in several image recovery and vision problems. The proposed approaches obtain sparse codes for each pixel in brain magnetic resonance images considering their intensity values and location information. Since it is trivial to obtain pixel-wise sparse codes, and combining multiple features in the sparse coding setup is not straightforward, we propose to perform sparse coding in a high-dimensional feature space where non-linear similarities can be effectively modeled. We use the training data from expert-segmented images to obtain kernel dictionaries with the kernel K-lines clustering procedure. For a test image, sparse codes are computed with these kernel dictionaries, and they are used to identify the tumor regions. This approach is completely automated, and does not require user intervention to initialize the tumor regions in a test image. Furthermore, a low complexity segmentation approach based on kernel sparse codes, which allows the user to initialize the tumor region, is also presented. Results obtained with both the proposed approaches are validated against manual segmentation by an expert radiologist, and the proposed methods lead to accurate tumor identification.

cs.CV↗

arXiv2013

Ensemble Sparse Models for Image Analysis

Sparse representations with learned dictionaries have been successful in several image analysis applications. In this paper, we propose and analyze the framework of ensemble sparse models, and demonstrate their utility in image restoration and unsupervised clustering. The proposed ensemble model approximates the data as a linear combination of approximations from multiple \textit{weak} sparse models. Theoretical analysis of the ensemble model reveals that even in the worst-case, the ensemble can perform better than any of its constituent individual models. The dictionaries corresponding to the individual sparse models are obtained using either random example selection or boosted approaches. Boosted approaches learn one dictionary per round such that the dictionary learned in a particular round is optimized for the training examples having high reconstruction error in the previous round. Results with compressed recovery show that the ensemble representations lead to a better performance compared to using a single dictionary obtained with the conventional alternating minimization approach. The proposed ensemble models are also used for single image superresolution, and we show that they perform comparably to the recent approaches. In unsupervised clustering, experiments show that the proposed model performs better than baseline approaches in several standard datasets.

cs.CV↗