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Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
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Cited by 1397 (38 self)
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? To recover x 0 , we consider the solution x to the 1 regularization problem where is the size of the error term e. We show that if A obeys a uniform uncertainty principle (with unitnormed columns) and if the vector x 0 is sufficiently sparse, then the solution is within the noise level As a first example
Using Geometric Blur for Point Correspondence
"... Abstract — In computer vision applications, point correspondence plays an important role. Here, we present a technique called geometric blur to find point correspondences between two different images, even in the presence of affine distortions. We compare the results of this technique with other pre ..."
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prevalent techniques for finding point correspondences, such as SSD (Sum of Squared Differences) with uniform Gaussian blur. Experimental results are shown on various face images and other object images. Index Terms — point correspondences, geometric blur, interest points, object detection and recognition
Examplebased superresolution
 IEEE COMPUT. GRAPH. APPL
, 2001
"... The Problem: Pixel representations for images do not have resolution independence. When we zoom into a bitmapped image, we get a blurred image. Figure 1 shows the problem for a teapot image, rich with realworld detail. We know the teapot’s features should remain sharp as we zoom in on them, yet sta ..."
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Cited by 349 (5 self)
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. Cubic spline interpolation [5] is a very common image interpolation function, but suffers from blurring of edges and image details. Recent attempts to improve on cubic spline interpolation [6, 8, 2] have met with limited success. Schreiber and collaborators [6] proposed a sharpened Gaussian interpolator
Sampling signals with finite rate of innovation
 IEEE Transactions on Signal Processing
, 2002
"... Abstract—Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials ..."
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Cited by 350 (67 self)
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polynomials. Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic
Removing camera shake from a single photograph
 ACM Trans. Graph
, 2006
"... Camera shake during exposure leads to objectionable image blur and ruins many photographs. Conventional blind deconvolution methods typically assume frequencydomain constraints on images, or overly simplified parametric forms for the motion path during camera shake. Real camera motions can follow c ..."
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Cited by 325 (16 self)
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convoluted paths, and a spatial domain prior can better maintain visually salient image characteristics. We introduce a method to remove the effects of camera shake from seriously blurred images. The method assumes a uniform camera blur over the image and negligible inplane camera rotation. In order
Mutual information and minimum meansquare error in Gaussian channels
 IEEE TRANS. INFORM. THEORY
, 2005
"... This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given the out ..."
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Cited by 288 (34 self)
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This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given
Restoration of a Single Superresolution Image from Several Blurred, Noisy, and Undersampled Measured Images
, 1997
"... The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodo ..."
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Cited by 267 (22 self)
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and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space and timevariant blur, the (additive Gaussian) noise, the different measured
Scalebased description and recognition of planar curves and twodimensional shapes
, 1986
"... The problem of finding a description, at varying levels of detail, for planar curves and matching two such descriptions is posed and solved in this paper. A number of necessary criteria are imposed on any candidate solution method. Pathbased Gaussian smoothing techniques are applied to the curve to ..."
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Cited by 213 (3 self)
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The problem of finding a description, at varying levels of detail, for planar curves and matching two such descriptions is posed and solved in this paper. A number of necessary criteria are imposed on any candidate solution method. Pathbased Gaussian smoothing techniques are applied to the curve
Removing NonUniform Motion Blur from Images ∗
"... We propose a method for removing nonuniform motion blur from multiple blurry images. Traditional methods focus on estimating a single motion blur kernel for the entire image. In contrast, we aim to restore images blurred by unknown, spatially varying motion blur kernels caused by different relative ..."
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Cited by 44 (3 self)
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We propose a method for removing nonuniform motion blur from multiple blurry images. Traditional methods focus on estimating a single motion blur kernel for the entire image. In contrast, we aim to restore images blurred by unknown, spatially varying motion blur kernels caused by different
Total Variation Blind Deconvolution
, 1996
"... In this paper, we present a blind deconvolution algorithm based on the total variational (TV) minimization method proposed in [11]. The motivation for regularizing with the TV norm is that it is extremely effective for recovering edges of images [11] as well as some blurring functions, e.g. motion b ..."
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Cited by 197 (15 self)
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blur) and both the image and the PSF can be recovered under the presence of high noise level. Finally, we remark that PSF's without sharp edges, e.g. Gaussian blur, can also be identified through the TV approach. I. Introduction It is wellknown that recovering the image u (resp. the PSF k
Results 1  10
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