Results 1  10
of
111,491
Interpolation of ShiftedLacunary Polynomials
, 2010
"... Given a “black box” function to evaluate an unknown rational polynomial f ∈ Q[x] at points modulo a prime p, we exhibit algorithms to compute the representation of the polynomial in the sparsest shifted power basis. That is, we determine the sparsity t ∈ Z>0, the shift α ∈ Q, the exponents 0 ≤ e1 ..."
Abstract
 Add to MetaCart
) representation size, which may be logarithmic in the degree of f. Our method combines previous celebrated results on sparse interpolation and computing sparsest shifts, and provides a way to handle polynomials with extremely high degree which are, in some sense, sparse in information.
Interpolation of ShiftedLacunary Polynomials (Extended Abstract)
"... Given a “black box” function to evaluate an unknown rational polynomial f ∈Q[x] at points modulo a prime p, we exhibit algorithms to compute the representation of the polynomial in the sparsest shifted power basis. That is, we determine the sparsity t∈Z>0, the shift α∈Q, the exponents 0≤e1< ..."
Abstract

Cited by 11 (1 self)
 Add to MetaCart
and in particular is logarithmic in deg f. Our method combines previous celebrated results on sparse interpolation and computing sparsest shifts, and provides a way to handle polynomials with extremely high degree which are, in some sense, sparse in information. We give both an unconditional deterministic algorithm
Bayesian Interpolation
 Neural Computation
, 1991
"... Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data. T ..."
Abstract

Cited by 721 (17 self)
 Add to MetaCart
Although Bayesian analysis has been in use since Laplace, the Bayesian method of modelcomparison has only recently been developed in depth. In this paper, the Bayesian approach to regularisation and modelcomparison is demonstrated by studying the inference problem of interpolating noisy data
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
Abstract

Cited by 496 (2 self)
 Add to MetaCart
. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
Factoring wavelet transforms into lifting steps
 J. Fourier Anal. Appl
, 1998
"... ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This dec ..."
Abstract

Cited by 573 (8 self)
 Add to MetaCart
ABSTRACT. This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is wellknown to algebraists (and expressed by the formula); it is also used in linear systems theory in the electrical engineering community. We present here a selfcontained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used in the biorthogonal, i.e, nonunitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a waveletlike transform that maps integers to integers. 1.
The Design and Use of Steerable Filters
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1991
"... Oriented filters are useful in many early vision and image processing tasks. One often needs to apply the same filter, rotated to different angles under adaptive control, or wishes to calculate the filter response at various orientations. We present an efficient architecture to synthesize filters of ..."
Abstract

Cited by 1079 (11 self)
 Add to MetaCart
Oriented filters are useful in many early vision and image processing tasks. One often needs to apply the same filter, rotated to different angles under adaptive control, or wishes to calculate the filter response at various orientations. We present an efficient architecture to synthesize filters of arbitrary orientations from linear combinations of basis filters, allowing one to adaptively "steer" a filter to any orientation, and to determine analytically the filter output as a function of orientation.
Image registration methods: a survey
 IMAGE AND VISION COMPUTING
, 2003
"... This paper aims to present a review of recent as well as classic image registration methods. Image registration is the process of overlaying images (two or more) of the same scene taken at different times, from different viewpoints, and/or by different sensors. The registration geometrically align t ..."
Abstract

Cited by 734 (9 self)
 Add to MetaCart
This paper aims to present a review of recent as well as classic image registration methods. Image registration is the process of overlaying images (two or more) of the same scene taken at different times, from different viewpoints, and/or by different sensors. The registration geometrically align two images (the reference and sensed images). The reviewed approaches are classified according to their nature (areabased and featurebased) and according to four basic steps of image registration procedure: feature detection, feature matching, mapping function design, and image transformation and resampling. Main contributions, advantages, and drawbacks of the methods are mentioned in the paper. Problematic issues of image registration and outlook for the future research are discussed too. The major goal of the paper is to provide a comprehensive reference source for the researchers involved in image registration, regardless of particular application areas.
Results 1  10
of
111,491