Related papers: Global Optimality in Separable Dictionary Learning…
The traditional sparse modeling approach, when applied to inverse problems with large data such as images, essentially assumes a sparse model for small overlapping data patches. While producing state-of-the-art results, this methodology is…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long…
We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of…
This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some…
Deep learning analyses have offered sensitivity leaps in detection of cognitive states from functional MRI (fMRI) measurements across the brain. Yet, as deep models perform hierarchical nonlinear transformations on their input, interpreting…
Classification methods based on sparse estimation have drawn much attention recently, due to their effectiveness in processing high-dimensional data such as images. In this paper, a method to improve the performance of a sparse…
Diffusion magnetic resonance imaging (dMRI) enables non-invasive investigation of tissue microstructure. The Standard Model (SM) of white matter aims to disentangle dMRI signal contributions from intra- and extra-axonal water compartments.…
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent…
We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…
The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…
In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…
We consider the problem of distributed dictionary learning, where a set of nodes is required to collectively learn a common dictionary from noisy measurements. This approach may be useful in several contexts including sensor networks.…
This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…
Dictionary learning algorithms have been successfully used for both reconstructive and discriminative tasks, where an input signal is represented with a sparse linear combination of dictionary atoms. While these methods are mostly developed…
The use of functional brain imaging for research and diagnosis has benefitted greatly from the recent advancements in neuroimaging technologies, as well as the explosive growth in size and availability of fMRI data. While it has been shown…
\hspace{2mm} Diffusion-weighted magnetic resonance imaging (dMRI) of the brain offers unique capabilities including noninvasive probing of tissue microstructure and structural connectivity. It is widely used for clinical assessment of…
Diffusion Magnetic Resonance Imaging (dMRI) plays a critical role in studying microstructural changes in the brain. It is, therefore, widely used in clinical practice; yet progress in learning general-purpose representations from dMRI has…
Diffusion Magnetic Resonance Imaging (dMRI) plays a crucial role in the noninvasive investigation of tissue microstructural properties and structural connectivity in the \textit{in vivo} human brain. However, to effectively capture the…