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Reconstruction of Signal from Samples of Its Integral in Spline Subspaces [chapter]

Jun Xian, Yongjin Li, Wei Lin
2004 Lecture Notes in Computer Science  
In this paper, we study the reconstructing of signals based on regular and irregular incremental integral samples in some nonbandlimited space--spline subspace, and we obtain reconstructing formulas with  ...  So we need to give the reconstruction of signal from samples of its integral. In this paper, we discuss the reconstruction of signal from samples of its integral in spline subspaces.  ...  Conclusion In this paper, we obtain reconstruction formula from samples of its integral in spline subspaces with the simple new method.  ... 
doi:10.1007/978-3-540-24687-9_75 fatcat:i2q3um7d25efxe6gjtteduova4

Reconstruction Algorithm of Signals from Special Samples in Spline Spaces [chapter]

Jun Xian, Degao Li
2005 Lecture Notes in Computer Science  
In this paper, we introduce integral sampling and study the reconstruction of signals based on non-uniform average samples in spline subspace.  ...  By using a new method, we obtain a new reconstruction formula.  ...  In this paper, we discuss the reconstruction of signal from samples of its integral in spline subspaces. The outline of this paper is in the following.  ... 
doi:10.1007/11428862_106 fatcat:bbvjt3qifjbupdzbwmxtqov7qa

Sampling and Reconstruction of Sparse Signals in Shift-Invariant Spaces: Generalized Shannon's Theorem Meets Compressive Sensing [article]

Tin Vlašić, Damir Seršić
2020 arXiv   pre-print
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces.  ...  The samples are subsequently filtered by a discrete-time correction filter in order to reconstruct expansion coefficients of an observed signal.  ...  RECONSTRUCTION OF SIGNALS IN SI SPACES FROM RD MEASUREMENTS The objective is to recover SI samples c k from a reduced set of linear measurements y k .  ... 
arXiv:2010.15618v1 fatcat:ifwmweeww5f43cadl2qgj7imfm

Generalizations of the sampling theorem: Seven decades after Nyquist

P.P. Vaidyanathan
2001 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
This paper presents some of the less known aspects of sampling, with special emphasis on non bandlimited signals, pointwise stability of reconstruction, and reconstruction from nonuniform samples.  ...  The sampling theorem is one of the most basic and fascinating topics in engineering sciences. The most well-known form is Shannon's uniform-sampling theorem for bandlimited signals.  ...  APPENDIX I BANDLIMITED SIGNALS: EVALUATING INTEGRALS FROM SUMS For a -BL signal it turns out that certain integrals can be calculated exactly by using sums of samples.  ... 
doi:10.1109/81.948437 fatcat:b7avsvcgjreupdbilnktebl5hq

A minimum squared-error framework for generalized sampling

Y.C. Eldar, T.G. Dvorkind
2006 IEEE Transactions on Signal Processing  
We treat the problem of reconstructing a signal from its nonideal samples where the sampling and reconstruction spaces as well as the class of input signals can be arbitrary subspaces of a Hilbert space  ...  To obtain a good approximation of the signal in the reconstruction space from its samples, we suggest two design strategies that attempt to minimize the squared-norm error between the signal and its reconstruction  ...  The reconstruction problem then becomes that of reconstructing a signal in from its orthogonal projection onto a subspace .  ... 
doi:10.1109/tsp.2006.873488 fatcat:ydumxthrf5cenmymcrnsbgw324

Single-Pixel Compressive Imaging in Shift-Invariant Spaces via Exact Wavelet Frames [article]

Tin Vlašić, Damir Seršić
2022 arXiv   pre-print
We reinterpret the acquisition procedure of a single-pixel camera as filtering of the observed signal with continuous-domain functions that lie in an SI subspace spanned by the integer shifts of the box  ...  Experimental results show that the proposed framework achieves a significant improvement of the reconstruction quality relative to the conventional discretization in CS setups.  ...  The authors are also grateful to the anonymous reviewers for their valuable comments and suggestions, which immensely helped improving the quality of the paper. Funding References  ... 
arXiv:2106.00404v2 fatcat:qhrbu5nebrd5nf6gvtf74fusoe

Weighted sampling and signal reconstruction in spline subspaces

Jun Xian, Shi-Ping Luo, Wei Lin
2006 Signal Processing  
In this paper, we construct reproducing kernel in spline subspaces and use the reproducing kernel to obtain reconstructions formula from the weighted samples and incremental integral samples.  ...  We also improve A-P iterative algorithm, and use the algorithm to implement the reconstruction from weighted samples, and obtain explicit convergence rate of the algorithm in spline subspaces.  ...  The work was partially done while the author Wei LIN was visiting the Institute for Mathematical Sciences, National University of Singapore in 2003. The visit was supported by the institute.  ... 
doi:10.1016/j.sigpro.2005.05.013 fatcat:4hhbtbraxjcktdzw6uizggtb5q

Subspace-based methods for image registration and super-resolution

Patrick Vandewalle, Loic Baboulaz, Pier Luigi Dragotti, Martin Vetterli
2008 2008 15th IEEE International Conference on Image Processing  
Then, we present three registration methods: one approach using ideas from variable projections, one using a Fourier description of the aliased signals, and one using a spline description of the sampling  ...  In this paper, we give an overview of some subspace techniques that address this problem. We first formulate super-resolution in a multichannel sampling framework with unknown offsets.  ...  The above equation is therefore showing that it is possible to retrieve the exact moments τ m,k of the signal f (t − t k ) from its samples.  ... 
doi:10.1109/icip.2008.4711837 dblp:conf/icip/VandewalleBDV08 fatcat:6mzu5f6o7bd5lgzzqlq6xzafa4

Page 715 of Mathematical Reviews Vol. , Issue 2001A [page]

2001 Mathematical Reviews  
Luc (B-GHNT-IT; Ghent); Olyslager, Frank (B-GHNT-IT; Ghent) Modified B-splines for the sampling of bandlimited functions.  ...  Further, we develop an effi- cient reconstruction mechanism, using the concept of a regularized solution, in which we penalize a candidate solution in proportion to its departure from a model which resembles  ... 

Consistent Sampling and Signal Recovery

A. Hirabayashi, M. Unser
2007 IEEE Transactions on Signal Processing  
The requirement is that the reconstructed signal is indistinguishable from the input in the sense that it yields the exact same measurements.  ...  The key idea is to exclude the null space of the sampling operator from the reconstruction space and to enforce consistency on its complement.  ...  SAMPLING THEOREM WITH PRESERVATION OF PREFERENTIAL SIGNALS In Theorem 2, we are free to choose the subspace as long as it is a complementary subspace of in .  ... 
doi:10.1109/tsp.2007.895996 fatcat:7mm6btomxfhitmgyog3cgcpxue

Nonideal Sampling and Regularization Theory

Sathish Ramani, Dimitri Van De Ville, Thierry Blu, Michael Unser
2008 IEEE Transactions on Signal Processing  
Shannon's sampling theory and its variants provide effective solutions to the problem of reconstructing a signal from its samples in some "shift-invariant" space, which may or may not be bandlimited.  ...  In this paper, we present some further justification for this type of representation, while addressing the issue of the specification of the best reconstruction space.  ...  INTRODUCTION S HANNON's sampling theory provides an elegant method to perfectly reconstruct bandlimited signals from their equidistant samples [1] - [5] .  ... 
doi:10.1109/tsp.2007.908997 fatcat:f7o67b5boveslimrsklu5nuiee

Spatial system identification of a simply supported beam and a trapezoidal cantilever plate

A.J. Fleming, S.O.R. Moheimani
2003 IEEE Transactions on Control Systems Technology  
For the purpose of control, system identification is often employed to estimate the dynamics from disturbance and command inputs to set of outputs.  ...  Such discretization of a spatially distributed system places unknown weightings on the control objective, in many cases, contradicting the original goal of optimal control.  ...  Ninness for their contributions in respect to construction of the experimental apparatus and system identification software.  ... 
doi:10.1109/tcst.2003.816415 fatcat:bpz4ia5xljfdthhkxzoojtgyfq

Sampling Moments and Reconstructing Signals of Finite Rate of Innovation: Shannon Meets Strang–Fix

Pier Luigi Dragotti, Martin Vetterli, Thierry Blu
2007 IEEE Transactions on Signal Processing  
Recently, it was shown that, by using an adequate sampling kernel and a sampling rate greater or equal to the rate of innovation, it is possible to reconstruct such signals uniquely [34].  ...  In this paper, we show that many signals with a finite rate of innovation can be sampled and perfectly reconstructed using physically realizable kernels of compact support and a local reconstruction algorithm  ...  It follows that: (15) where, in , we have used (14) , and follows from integration by parts.  ... 
doi:10.1109/tsp.2006.890907 fatcat:blj3vegcargypplkxtyeezai4u

Local average sampling and reconstruction with fundamental splines of fractional order [article]

P. Devaraj, P. Massopust, S. Yugesh
2019 arXiv   pre-print
We analyse sampling and average sampling techniques for fractional spline subspaces of L^2(R).  ...  Fractional B-splines β_σ are extensions of Schoenberg's polynomial splines of integral order to real order σ > -1.  ...  Acknowledgement:-The third author would like to thank the management of Sri Sivasubramaniya Nadar College of Engineering. The second author was partially supported by DFG grant MA 5801/2-1.  ... 
arXiv:1904.03434v1 fatcat:7lc5togsbvadxn2eulqr62qejm

Robust multiresolution techniques for image reconstruction

Michael Liebling, Alexander A. Oraevsky, Lihong V. Wang
2007 Photons Plus Ultrasound: Imaging and Sensing 2007: The Eighth Conference on Biomedical Thermoacoustics, Optoacoustics, and Acousto-optics  
The reconstruction of images from projections, diffraction fields, or other similar measurements requires applying signal processing techniques within a physical context.  ...  Although modeling of the acquisition procedure can conveniently be carried out in the continuous domain, actual reconstruction from experimental measurements requires the derivation of discrete algorithms  ...  ACKNOWLEDGMENTS Michael Liebling is supported by a fellowship from the Swiss National Science Foundation no. PA002-111433.  ... 
doi:10.1117/12.701352 fatcat:hcutip3m6rbw7oat3wlydefeh4
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