## A Computationally Efficient Superresolution Image Reconstruction Algorithm (2000)

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Citations: | 52 - 4 self |

### BibTeX

@MISC{Nguyen00acomputationally,

author = {Nhat Nguyen and Peyman Milanfar and Gene Golub},

title = {A Computationally Efficient Superresolution Image Reconstruction Algorithm},

year = {2000}

}

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### Abstract

Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution had not adequately addressed the computational and numerical issues for this ill-conditioned and typically underdetermined large scale problem. We propose efficient block circulant preconditioners for solving the Tikhonov-regularized superresolution problem by the conjugate gradient method. We also extend to underdetermined systems the derivation of the generalized cross-validation method for automatic calculation of regularization parameters. Effectiveness of our preconditioners and regularization techniques is demonstrated with superresolution results for a simulated sequence and a forward looking infrared (FLIR) camera image sequence.

### Citations

1518 | Iterative methods for sparse linear systems - Saad - 2003 |

701 | A survey of image registration techniques
- Brown
- 1992
(Show Context)
Citation Context ...by a single motion vector. In the case where the scene motions are controlled, the motion vectors are known. Otherwise, they may be estimated by some image registration algorithm; see survey by Brown =-=[5]-=-. For completeness, we include in Appendix A a simple algorithm we used to compute scene motion vectors. We will assume that the point spread function (PSF) which generates the blurring operator is kn... |

494 | Iterative Solution Methods - Axelsson - 1994 |

273 |
Generalized cross-validation as a method for choosing a good ridge parameter
- Golub, Heath, et al.
- 1979
(Show Context)
Citation Context ...to calculate regularization parameters for Tikhonov-regularized overdetermined least squares problems without accurate knowledge of the variance of noise, to our underdetermined problem. Golub et al. =-=[14]-=- suggested that GCV can be used for underdetermined problems, and McIntosh and Veronis [24] successfully implemented GCV for their underdetermined tracer inverse problems. However, since the derivatio... |

261 |
Improving resolution by image registration
- Irani, Peleg
- 1991
(Show Context)
Citation Context ...ier S 1057-7149(01)01664-5. 1057–7149/01$10.00 © 2001 IEEE whose intersection contains the HR estimate and successively projected an arbitrary initial estimate onto these constraint sets. Others [4], =-=[20]-=-, [23] adopted a related method, the iterative back-projection method, frequently used in computer aided tomography. Cheeseman et al. [9] used the standard Jacobi’s method, and Hardie et al. [18] prop... |

210 | Extraction of highresolution frames from video sequences
- Schultz, Stevenson
- 1996
(Show Context)
Citation Context ...EEE, and Gene Golub Abstract—Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution [9], [11], [18], [27], =-=[30]-=- had not adequately addressed the computational and numerical issues for this ill-conditioned and typically underdetermined large scale problem. We propose efficient block circulant preconditioners fo... |

207 | Restoration of a single superresolution image from several blurred, noisy, and undersampled measured images
- Elad, Feuer
- 1997
(Show Context)
Citation Context ..., Senior Member, IEEE, and Gene Golub Abstract—Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution [9], =-=[11]-=-, [18], [27], [30] had not adequately addressed the computational and numerical issues for this ill-conditioned and typically underdetermined large scale problem. We propose efficient block circulant ... |

188 |
Multiframe image restoration and registration
- Tsai, Huang
- 1984
(Show Context)
Citation Context ...erresolution: the reconstruction of a high-resolution (HR) unaliased image from several low-resolution (LR) aliased images. Proposed direct methods include Fourier domain approaches by Tsai and Huang =-=[34]-=-, Tekalp et al. [33], [27], [26], and Kim et al. [22], [21] where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods [29], [1] have used an interpo... |

157 | Joint map registration and high-resolution image estimation using a sequence of undersampled images
- Hardie, Barnard, et al.
- 1997
(Show Context)
Citation Context ...or Member, IEEE, and Gene Golub Abstract—Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution [9], [11], =-=[18]-=-, [27], [30] had not adequately addressed the computational and numerical issues for this ill-conditioned and typically underdetermined large scale problem. We propose efficient block circulant precon... |

140 |
R.:“ Digital Image Restoration
- Andrews, Hunt, et al.
(Show Context)
Citation Context ...RIZATION The PSF is derived from the discretization of a compact operator (i.e., the image of every -bounded sequence of functions has at least one converging subsequence [16]), so is ill-conditioned =-=[2]-=-. Thus, even small changes in can result in wild oscillations in approximations to when (2) is solved directly. To obtain a reasonable estimate for we reformulate the problem as a regularized minimiza... |

131 | Conjugate gradient methods for Toeplitz systems
- Chan, Ng
- 1996
(Show Context)
Citation Context ...ding preconditioners for standard banded Toeplitz matrices in the following subsection. Extensions of these preconditioners and their convergence properties to the block case are then straightforward =-=[7]-=-. A. Circulant Preconditioners The first preconditioner, originally developed by Strang [8], completes a Toeplitz matrix by copying the central diagonals. For an upper triangular banded Toeplitz matri... |

128 | Super-resolution Video Reconstruction with Arbitrary Sampling Latices and Nonzero Aperture Time
- Patti, Sezan, et al.
- 1997
(Show Context)
Citation Context ...ber, IEEE, and Gene Golub Abstract—Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution [9], [11], [18], =-=[27]-=-, [30] had not adequately addressed the computational and numerical issues for this ill-conditioned and typically underdetermined large scale problem. We propose efficient block circulant precondition... |

117 | Virtual bellows: Constructing high-quality images from video
- Mann, Picard
- 1994
(Show Context)
Citation Context ...1057-7149(01)01664-5. 1057–7149/01$10.00 © 2001 IEEE whose intersection contains the HR estimate and successively projected an arbitrary initial estimate onto these constraint sets. Others [4], [20], =-=[23]-=- adopted a related method, the iterative back-projection method, frequently used in computer aided tomography. Cheeseman et al. [9] used the standard Jacobi’s method, and Hardie et al. [18] proposed a... |

106 |
Recursive reconstruction of high resolution image from noisy undersampled multiframes
- Kim, Bose, et al.
- 1990
(Show Context)
Citation Context ...unaliased image from several low-resolution (LR) aliased images. Proposed direct methods include Fourier domain approaches by Tsai and Huang [34], Tekalp et al. [33], [27], [26], and Kim et al. [22], =-=[21]-=- where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods [29], [1] have used an interpolation-restoration combination approach in the image domain... |

97 | Super-resolved surface reconstruction from multiple images, NASA
- Cheeseman, Kanefsky, et al.
- 1994
(Show Context)
Citation Context ...anfar, Senior Member, IEEE, and Gene Golub Abstract—Superresolution reconstruction produces a high-resolution image from a set of low-resolution images. Previous iterative methods for superresolution =-=[9]-=-, [11], [18], [27], [30] had not adequately addressed the computational and numerical issues for this ill-conditioned and typically underdetermined large scale problem. We propose efficient block circ... |

94 |
Regularization methods for large-scale problems
- Hanke, Hansen
- 1993
(Show Context)
Citation Context ...quent submission. III. REGULARIZATION The PSF is derived from the discretization of a compact operator (i.e., the image of every -bounded sequence of functions has at least one converging subsequence =-=[16]-=-), so is ill-conditioned [2]. Thus, even small changes in can result in wild oscillations in approximations to when (2) is solved directly. To obtain a reasonable estimate for we reformulate the probl... |

87 | Motion deblurring and super-resolution from an image sequence
- BASCLE, BLAKE, et al.
- 1996
(Show Context)
Citation Context ...entifier S 1057-7149(01)01664-5. 1057–7149/01$10.00 © 2001 IEEE whose intersection contains the HR estimate and successively projected an arbitrary initial estimate onto these constraint sets. Others =-=[4]-=-, [20], [23] adopted a related method, the iterative back-projection method, frequently used in computer aided tomography. Cheeseman et al. [9] used the standard Jacobi’s method, and Hardie et al. [18... |

85 |
Improved resolution from sub-pixel shifted pictures
- Ur, Gross
- 1992
(Show Context)
Citation Context ...quency information is extracted from low-frequency data in the given LR frames. Several methods [29], [1] have used an interpolation-restoration combination approach in the image domain. Ur and Gross =-=[35]-=- and Shekarforoush and Chellappa [31] considered superresolution as generalized sampling problem with periodic samples. In this paper, we are mainly interested in the computational issue for iterative... |

69 |
High-resolution image reconstruction from lower-resolution image sequences and space-varying image restoration
- Tekalp, Ozkan, et al.
- 1992
(Show Context)
Citation Context ...construction of a high-resolution (HR) unaliased image from several low-resolution (LR) aliased images. Proposed direct methods include Fourier domain approaches by Tsai and Huang [34], Tekalp et al. =-=[33]-=-, [27], [26], and Kim et al. [22], [21] where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods [29], [1] have used an interpolation-restoration c... |

67 |
High-resolution image recovery from image-plane arrays, using convex projections
- Stark, Oskoui
- 1989
(Show Context)
Citation Context ...amples. In this paper, we are mainly interested in the computational issue for iterative methods. Projection type methods have been used by several researchers. Patti et al. [27] and Stark and Oskoui =-=[32]-=- proposed projection onto convex sets (POCS) algorithms, which defined sets of closed convex constraints Manuscript received June 8, 1999; revised November 16, 2000. This work was supported in part by... |

67 |
der Vorst. The rate of convergence of conjugate gradients
- Sluis, van
- 1986
(Show Context)
Citation Context ... superresolution is computationally intensive. The number of unknowns, the same as the number of pixels in the HR image, is typically in the tens or hundreds of thousands. The convergence rate for CG =-=[36]-=- is dependent on the distribution of eigenvalues of the system matrix. The method works well on matrices that are either well-conditioned or have just a few distinct eigenvalues; see [15, p. 525]. Pre... |

51 |
A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
- Hutchinson
- 1990
(Show Context)
Citation Context ...tivation here is that since approximates well, should be close to . Even so, calculating the term tr exactly is still infeasible. Therefore, we use the unbiased trace estimator proposed by Hutchinson =-=[19]-=-. Let be a discrete random variable which takes the values and each with probability , and let be a vector whose entries are independent samples from . Then the term is an unbiased estimator of tr . S... |

46 |
Recursive high-resolution reconstruction of blurred multiframe images
- Kim, Su
- 1993
(Show Context)
Citation Context ... (HR) unaliased image from several low-resolution (LR) aliased images. Proposed direct methods include Fourier domain approaches by Tsai and Huang [34], Tekalp et al. [33], [27], [26], and Kim et al. =-=[22]-=-, [21] where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods [29], [1] have used an interpolation-restoration combination approach in the image ... |

43 |
Toeplitz equations by conjugate gradients with circulant preconditioner
- Chan, Strang
- 1989
(Show Context)
Citation Context ...ensions of these preconditioners and their convergence properties to the block case are then straightforward [7]. A. Circulant Preconditioners The first preconditioner, originally developed by Strang =-=[8]-=-, completes a Toeplitz matrix by copying the central diagonals. For an upper triangular banded Toeplitz matrix . .. the preconditioner is simply . . .. . .. For a block matrix with Toeplitz blocks , t... |

31 |
Iterative reconstruction of band-limited images from nonuniformly spaced samples
- Sauer, Allebach
- 1987
(Show Context)
Citation Context ...roaches by Tsai and Huang [34], Tekalp et al. [33], [27], [26], and Kim et al. [22], [21] where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods =-=[29]-=-, [1] have used an interpolation-restoration combination approach in the image domain. Ur and Gross [35] and Shekarforoush and Chellappa [31] considered superresolution as generalized sampling problem... |

24 | Data-driven multichannel superresolution with application to video sequences
- Shekarforoush, Chellappa
- 1999
(Show Context)
Citation Context ...low-frequency data in the given LR frames. Several methods [29], [1] have used an interpolation-restoration combination approach in the image domain. Ur and Gross [35] and Shekarforoush and Chellappa =-=[31]-=- considered superresolution as generalized sampling problem with periodic samples. In this paper, we are mainly interested in the computational issue for iterative methods. Projection type methods hav... |

15 | Generalized cross-validation for large scale problems - Golub, Matt - 1997 |

13 | The rate of convergence of conjugate gradients - SLUIS, VORST - 1986 |

12 | Super-resolution reconstruction of images - Elad - 1996 |

8 |
Toeplitz approximate inverse preconditioner for banded Toeplitz matrices
- Hanke, Nagy
- 1994
(Show Context)
Citation Context ...s problem, , with block Toeplitz matrix , we precondition with , where is the block preconditioner as described above. . .. . .. . .. . .. . . . Our second preconditioner, developed by Hanke and Nagy =-=[17]-=-, is an approximate inverse preconditioner for an upper banded Toeplitz matrix with bandwidth less than or equal to . It is constructed as follows. First we embed into an circulant matrix according to... |

7 |
Acquisition of very high resolution images using stereo cameras
- Aizawa, Komatsu, et al.
- 1991
(Show Context)
Citation Context ...s by Tsai and Huang [34], Tekalp et al. [33], [27], [26], and Kim et al. [22], [21] where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods [29], =-=[1]-=- have used an interpolation-restoration combination approach in the image domain. Ur and Gross [35] and Shekarforoush and Chellappa [31] considered superresolution as generalized sampling problem with... |

6 | Preconditioned iterative methods for high-resolution image reconstruction with multisensors
- Chan, Chan, et al.
- 1998
(Show Context)
Citation Context ...t to noise and allow some modeling flexibility, projection-based algorithms are also known for their low rate of convergence. More recently, Hardie et al. [18], Connolly and Lane [10] and Chan et al. =-=[6]-=- have considered conjugate gradient (CG) methods for Tikhonov regularized superresolution. However, to a large degree, computational and numerical difficulties of superresolution have not been address... |

6 |
Image sequence restoration and de-interlacing by motion compensated Kalman filtering
- Patti, Sezan
- 1991
(Show Context)
Citation Context ... of a high-resolution (HR) unaliased image from several low-resolution (LR) aliased images. Proposed direct methods include Fourier domain approaches by Tsai and Huang [34], Tekalp et al. [33], [27], =-=[26]-=-, and Kim et al. [22], [21] where high-frequency information is extracted from low-frequency data in the given LR frames. Several methods [29], [1] have used an interpolation-restoration combination a... |

5 |
Numerical Techniques for Image Superresolution
- Nguyen
- 2000
(Show Context)
Citation Context ...em of equations above is underdetermined. The techniques presented here can be extended to the more general framework to allow for any shifts. This extension is addressed in the first author’s thesis =-=[25]-=-. For each frame , we approximate the relative motions between that frame and a reference frame by a single motion vector. In the case where the scene motions are controlled, the motion vectors are kn... |

3 | A stochastic estimator of the trace of the in matrix for Laplacian smoothing splines - Hutchinson - 1990 |

3 | Blur Identi by the Method of Generalized Cross-Validation - Reeves, Mersereau - 1997 |

1 |
Gradient Methods for Superresolution
- Connolly, Lane
- 1997
(Show Context)
Citation Context ...hey are usually robust to noise and allow some modeling flexibility, projection-based algorithms are also known for their low rate of convergence. More recently, Hardie et al. [18], Connolly and Lane =-=[10]-=- and Chan et al. [6] have considered conjugate gradient (CG) methods for Tikhonov regularized superresolution. However, to a large degree, computational and numerical difficulties of superresolution h... |

1 |
Solving Underdetermined Tracer Inverse Problems by Spatial Smoothing and Cross Validation
- Mcintosh, Veronis
- 1993
(Show Context)
Citation Context ...s problems without accurate knowledge of the variance of noise, to our underdetermined problem. Golub et al. [14] suggested that GCV can be used for underdetermined problems, and McIntosh and Veronis =-=[24]-=- successfully implemented GCV for their underdetermined tracer inverse problems. However, since the derivation for the GCV formulation by Golub, Heath, and Wahba [14] applies only for overdetermined l... |

1 | Super-Resolution Reconstruction of Images, Ph. D. Thesis - The Technion - Elad - 1996 |