Currently, all major implementations of cyclotomic fields as well as number fields, are based on a dense model where elements are represented either as dense polynomials in the generator of the field or as coefficient vectors with respect to a fixed basis. While this representation allows for the asymptotically fastest arithmetic for general elements, it is unsuitable for fields of degree > 10 ...

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation is limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges or contours) that are very important elements in visual perception, ...

Sparse representation can efficiently model signals in different applications to facilitate processing. In this article, we will discuss various applications of sparse representation in wireless communications, with focus on the most recent compressive sensing (CS) enabled approaches. With the help of the sparsity property, CS is able to enhance the spectrum efficiency and energy efficiency for...

We derive a new deterministic algorithm for the computation of a sparse Legendre expansion f of degree N with M N nonzero terms from only 2M function resp. derivative values f (1), j = 0, . . . , 2M − 1 of this expansion. For this purpose we apply a special annihilating filter method that allows us to separate the computation of the indices of the active Legendre basis polynomials and the evalu...

In this paper we describe a new class of multidimensional representation systems, called shearlets. They are obtained by applying the actions of dilation, shear transformation and translation to a fixed function, and exhibit the geometric and mathematical properties, e.g., directionality, elongated shapes, scales, oscillations, recently advocated by many authors for sparse image processing appl...

Abstract: Sparse representation of data has grown rapidly in signal processing. The benefits of sparse regularization are economy of representation of many different varieties of data, as well as control of difficult aspects of inverse problems, e.g., regularization of ill-conditioned inverse problems. Herein we represent atmospheric turbulence point-spread-functions by training optimal overcom...

To better select the correct training sample and obtain the robust representation of the query sample, this paper proposes a discriminant-based sparse optimization learning model. This learning model integrates discriminant and sparsity together. Based on this model, we then propose a classifier called locality-based discriminant sparse representation (LDSR). Because discriminant can help to in...

Face recognition via sparse representation-based classification has received more and more attention in recent years. This approach has achieved state-of-the-art results, which outperforms traditional methods, especially when face image pixels are corrupted or occluded. In this paper, we propose a new weighted sparse representation method called WSRC-MSLBP which utilizes the multi-scale LBP (MS...

Sparse coding is a method for nding a representation of data in which each of the components of the representation is only rarely signiicantly active. Such a representation is closely related to redundancy reduction and independent component analysis, and has some neurophysiological plausibility. In this paper, we show how sparse coding can be used for denoising. Using maximum likelihood estima...