Reconstructing Signals with Finite Rate of Innovation from Noisy Samples

Bi, Ning; Nashed, M. Zuhair; Sun, Qiyu

doi:10.1007/s10440-009-9474-9

Cited by 23 publications

(19 citation statements)

References 32 publications

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“…In our formulation, the problem of recovering the EPI from a single swiped image is mapped to that of reconstructing signals with a finite rate of innovation (FRI) [22][23][24][25][26] . We demonstrate that the exact recovery of the EPI is possible when the scene is made of a single fronto-parallel plane with a texture pasted onto it that is a sum of sinusoids.…”

Section: 3mentioning

confidence: 99%

“…I I (v) is a piecewise signal in which each segment is a sum of sinusoids; it can therefore be recovered from the pixels p[k] using FRI theory [22][23][24][25][26][27] . It is assumed here that the point spread function ϕ(v) is an exponential reproducing kernel, as in FRI theory 25 , but less restrictive choices are also available 26 .…”

Section: Epi Recovery From a Swiped Imagementioning

confidence: 99%

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Capturing the plenoptic function in a swipe

Lawson

Brookes

Dragotti

2016

Applications of Digital Image Processing XXXIX

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Blur in images, caused by camera motion, is typically thought of as a problem. The approach described in this paper shows instead that it is possible to use the blur caused by the integration of light rays at different positions along a moving camera trajectory to extract information about the light rays present within the scene. Retrieving the light rays of a scene from different viewpoints is equivalent to retrieving the plenoptic function of the scene. In this paper, we focus on a specific case in which the blurred image of a scene, containing a flat plane with a texture signal that is a sum of sine waves, is analysed to recreate the plenoptic function. The image is captured by a single lens camera with shutter open, moving in a straight line between two points, resulting in a swiped image. It is shown that finite rate of innovation sampling theory can be used to recover the scene geometry and therefore the epipolar plane image from the single swiped image. This epipolar plane image can be used to generate unblurred images for a given camera location.

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Section: 3mentioning

confidence: 99%

Section: Epi Recovery From a Swiped Imagementioning

confidence: 99%

Capturing the plenoptic function in a swipe

Lawson

Brookes

Dragotti

2016

Applications of Digital Image Processing XXXIX

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show abstract

“…Unlike the compressed sampling or learning theory discussed earlier, in this situation the class C consists of infinite dimensional subspaces of H = 2 and therefore are more difficult to deal with even for a single shift-invariant subspace model ( = 1) [68]. The case in which a signal model is not a single subspace but a union of several of such subspaces is natural as in the case of signals with finite rate of innovation [69][70][71][72][73].…”

Section: Connection To Signalmentioning

confidence: 99%

A Review of Subspace Segmentation: Problem, Nonlinear Approximations, and Applications to Motion Segmentation

Aldroubi

2013

ISRN Signal Processing

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The subspace segmentation problem is fundamental in many applications. The goal is to cluster data drawn from an unknown union of subspaces. In this paper we state the problem and describe its connection to other areas of mathematics and engineering. We then review the mathematical and algorithmic methods created to solve this problem and some of its particular cases. We also describe the problem of motion tracking in videos and its connection to the subspace segmentation problem and compare the various techniques for solving it.

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“…The locally finitely-generated space V( ) in (2.6) was introduced in [44] to model signals with finite rate of innovations (see [8,34,43,47] and extensive references therein for the study of sampling for signals with finite rate of innovations). A model space of locally finitely-generated spaces is the shiftinvariant space V(φ 1 , .…”

Section: Theorem 21 Let V Be a Linear Space Of Functions On The Linementioning

confidence: 99%

Local reconstruction for sampling in shift-invariant spaces

Sun

2008

Adv Comput Math

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The local reconstruction from samples is one of most desirable properties for many applications in signal processing, but it has not been given as much attention. In this paper, we will consider the local reconstruction problem for signals in a shift-invariant space. In particular, we consider finding sampling sets X such that signals in a shift-invariant space can be locally reconstructed from their samples on X. For a locally finite-dimensional shiftinvariant space V we show that signals in V can be locally reconstructed from its samples on any sampling set with sufficiently large density. For a shiftinvariant space V(φ 1 , . . . , φ N ) generated by finitely many compactly supported functions φ 1 , . . . , φ N , we characterize all periodic nonuniform sampling sets X such that signals in that shift-invariant space V(φ 1 , . . . , φ N ) can be locally reconstructed from the samples taken from X. For a refinable shift-invariant space V(φ) generated by a compactly supported refinable function φ, we prove that for almost all (x 0 , x 1 ) ∈ [0, 1] 2 , any signal in V(φ) can be locally reconstructed from its samples from {x 0 , x 1 } + Z with oversampling rate 2. The proofs of our results on the local sampling and reconstruction in the refinable shift-invariant space V(φ) depend heavily on the linear independent shifts of a refinable function on measurable sets with positive Lebesgue measure and the almost ripplet property for a refinable function, which are new and interesting by themselves.

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Reconstructing Signals with Finite Rate of Innovation from Noisy Samples

Cited by 23 publications

References 32 publications

Capturing the plenoptic function in a swipe

Capturing the plenoptic function in a swipe

A Review of Subspace Segmentation: Problem, Nonlinear Approximations, and Applications to Motion Segmentation

Local reconstruction for sampling in shift-invariant spaces

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