Constrained total least‐squares computations for high‐resolution image reconstruction with multisensors

Ng, Michael K.; Koo, Jaehoon; Bose, N.K.

doi:10.1002/ima.10004

Cited by 64 publications

(29 citation statements)

References 15 publications

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“…, (17) with P N dimensional vectors w , ∀z ≥ 0, w > 0, (details can be found in [5,6]) that these functionals are lower bounds of the image priors p l (x|α l ), for l = 2, 3, in Eqs. (6) and (7) respectively.…”

Section: Variational Bayesian Inferencementioning

confidence: 99%

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Bayesian combination of sparse and non-sparse priors in image super resolution

Villena¹,

Vega²,

Babacan³

et al. 2013

Digital Signal Processing

105

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In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the 1 norm of horizontal and vertical first order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (SAR) prior. Since, for a given observation model, each prior produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational approximation will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of Kullback-Leibler (KL) divergences. We find this distribution in closed form. The estimated HR images are compared with the ones obtained by other SR reconstruction methods.

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Section: Variational Bayesian Inferencementioning

confidence: 99%

“…The limited accuracy inherent to HR registration from LR images is a shortcoming of this first approach. The second approach is to alternate between HR image registration and HR image estimation (see [5,[16][17][18][19][20][21][22][23][24][25]). …”

Section: Introductionmentioning

confidence: 99%

Bayesian combination of sparse and non-sparse priors in image super resolution

Villena¹,

Vega²,

Babacan³

et al. 2013

Digital Signal Processing

105

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show abstract

“…The main result there is to define convex sets which represent tight constraints on the solution to improve the results. Ng et al developed a regularized, constrained total least squares solution to obtain a highresolution image [5]. They consider the presence of perturbation errors of displacements around the ideal sub-pixel locations in addition to noisy observations.…”

Section: Literature Reviewmentioning

confidence: 99%

Super Resolution Imaging Applied to Scientific Images

Chaudhuri¹

2007

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. REPORT DATE JUL 20072. REPORT TYPE The final version of the code is being delivered along with this report. Also, the latest code and the results of the feasibility studies are being sent to the AFRL/ML collaborators. Dr. Seetharaman also visited IIT Bombay during April 16-30, 2007 on a related research mission and had an opportunity to verify and be trained on using the developed computer programs.The contract was to investigate the feasibility of super resolution imaging of large surfaces at nano-scale resolution. Four different techniques were considered for this study, and the computational results indicate a promising performance with a peak PSNR gain of 6 db over standard bilinear interpolation. In some cases, even a scale factor of 4 produced reliable results. Specifically the effort included: (1) a thorough survey of the state of the art, (2) data collected by US collaborators and analyzed by the investigator, (3) development of Papoulis-Gerchberg method to implement the analytic continuation of spectral details, (4) exploration of contourlet and its variant known as the Laplacian Edge model. Additionally, we developed a new technique for super resolution of material images known as total variation optimized image interpolation. The deliverance of this report serves to meet the fifth objective of the original contract.Place: Mumbai

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“…Iterative spatial domain methods are popular class of methods for solving the problems of resolution enhancement [2,19,20,21,24,30,34,37,38,41]. The problems are formulated as Tikhonov regularization.…”

Section: Introductionmentioning

confidence: 99%

High‐resolution image reconstruction with displacement errors: A framelet approach

Chan¹,

Riemenschneider²,

Shen³

et al. 2004

Int J Imaging Syst Tech

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High-resolution image reconstruction arises in many applications, such as remote sensing, surveillance, and medical imaging. The model of Bose and Boo [2] can be viewed as the passage of the high-resolution image through a blurring kernel built from the tensor product of a univariate low-pass filter of the form 1 2 + , 1, · · · , 1, 1 2 − , where is the displacement error. When the number L of low-resolution sensors is even, tight frame symmetric framelet filters were constructed in [8] from this low-pass filter using the unitary extension principle of [43]. The framelet filters do not depend on , and hence the resulting algorithm reduces to that of the case where = 0. Furthermore, the framelet method works for symmetric boundary conditions. This greatly simplifies the algorithm. However, both the design of the tight framelets and extension to symmetric boundary are only for even L and cannot be applied to the case when L is odd. In this paper, we design tight framelets and derive a tight framelet algorithm with symmetric boundary conditions that work for both odd and even L. An analysis of the convergence of the algorithms is also given. The details of the implementations of the algorithm are also given.

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Constrained total least‐squares computations for high‐resolution image reconstruction with multisensors

Cited by 64 publications

References 15 publications

Bayesian combination of sparse and non-sparse priors in image super resolution

Bayesian combination of sparse and non-sparse priors in image super resolution

Super Resolution Imaging Applied to Scientific Images

High‐resolution image reconstruction with displacement errors: A framelet approach

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