We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples y, y, . . . , y into an appropriate basis (dictionary) A∗ and sparse vectors x1∗, . . . , xn∗. Our algorithm is a simple alternating minimization procedure that switches between l1 minimization and gradient ...

Dictionary learning is a method to learn dictionary items adapted to data of a given distribution. It is shown that dictionary learned from data is more suited for vision task than universal dictionaries [4]. Traditionally, Vector Quantization (VQ), or using k-means to learn data cluster centroids, is a simple and popular method in the bag-of-features framework [5]. Recently, sparse coding is u...

Existing dictionary learning algorithms rely heavily on the assumption that the data points are vectors in some Euclidean space R, and the dictionary is learned from the input data using only the vector space structure of R. However, in many applications, features and data points often belong to some Riemannian manifold with its intrinsic metric structure that is potentially important and criti...

Many recent efforts have shown the effectiveness of dictionary learning methods in solving several computer vision problems. However, when designing dictionaries, training and testing domains may be different, due to different view points and illumination conditions. In this paper, we present a function learning framework for the task of transforming a dictionary learned from one visual domain ...

It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of purely reconstructive ones. This paper proposes a new step in that direction, with a novel sparse representation for signals belonging to different classes in...

Discriminative dictionary learning aims to learn a dictionary from training samples to enhance the discriminative capability of their coding vectors. Several discrimination terms have been proposed by assessing the prediction loss (e.g., logistic regression) or class separation criterion (e.g., Fisher discrimination criterion) on the coding vectors. In this paper, we provide a new insight on di...

While multitask learning has been extensively studied, most existing methods rely on linear models (e.g. linear regression, logistic regression), which may fail in dealing with more general (nonlinear) problems. In this paper, we present a new approach that combines dictionary learning with gradient boosting to achieve multitask learning with general (nonlinear) basis functions. Specifically, f...

We propose a new approach to reconstructing ECG signal from undersampled data based on constructing a combined overcomplete dictionary. The dictionary is obtained by combining the trained dictionary by K-SVD dictionary learning algorithm with universal types of dictionary such as DCT or wavelet basis. Using the trained overcomplete dictionary, the proposed method can find sparse approximation b...

Matrix factorization algorithms are emerging as popular tools in many applications, especially dictionary learning method for recovering biomedical image data from noisy and ill-conditioned measurements. We introduce a novel dictionary learning algorithm based on augmented Lagrangian (AL) approach to learn dictionaries from exemplar data and it can be extended to general matrix factorization pr...