Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional setting. Under mild technical conditions, we first establish the optimal rates of convergence for estimating the principal subspace which are sharp with respect to...

Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved using a recently introduced tree-structured sparse regularization norm, which has proven useful in several applications. This norm leads to regularized problems ...

In this paper, we present Adaptive Hierarchical Sensing (AHS), a novel adaptive hierarchical sensing algorithm for sparse signals. For a given but unknown signal with a sparse representation in an orthogonal basis, the sensing task is to identify its non-zero transform coefficients by performing only few measurements. A measurement is simply the inner product of the signal and a particular meas...

JPEG is one of the most widely used image compression method, but it causes annoying blocking artifacts at low bit-rates. Sparse representation is an efficient technique which can solve many inverse problems in image processing applications such as denoising and deblocking. In this paper, a post-processing method is proposed for reducing JPEG blocking effects via sparse representation. In this ...

Surface approximation with smooth functions suffers the problems of choosing the basis functions and representing non-smooth features. In this work, we introduce a sparse representation for surfaces with a set of redundant basis functions, which efficiently overcomes the overfitting artifacts. Moreover, we propose an approach of parameterization transformation, which makes the possibility to re...

Image-based classification of tissue histology, in terms of different components (e.g., subtypes of aberrant phenotypic signatures), provides a set of indices for tumor composition. Subsequently, integration of these indices in whole slide images (WSI), from a large cohort, can provide predictive models of the clinical outcome. However, the performance of the existing histology-based classifica...

It is well-known that the computation cost to nd the transitive closure (TC) of a graph stored as an adjacency matrix is the same, to within a constant factor, as matrix multiplication. In this paper, we present a new TC algorithm based on double hashing and two-dimensionally organized les. We show that, when using this algorithm, the computation and i/o costs of nding the TC of a database rela...

iris recognition is one of the most reliable methods for identification. in general, itconsists of image acquisition, iris segmentation, feature extraction and matching. among them, iris segmentation has an important role on the performance of any iris recognition system. eyes nonlinear movement, occlusion, and specular reflection are main challenges for any iris segmentation method. in this pa...

We formulate and derive a generalization of an orthogonal rationalfunction basis for spectral expansions over the infinite or semi-infinite interval. The original functions, first presented by Wiener, are a mapping and weighting of the Fourier basis to the infinite interval. By identifying the Fourier series as a biorthogonal composition of Jacobi polynomials/functions, we are able to define ge...