A blind image restoration system using higher-order statistics and Radon transform

Hussein, Aqbaal; Mashali, Samia A.; Mohamed, A.H.

doi:10.1109/icecs.1998.814068

Cited by 5 publications

(3 citation statements)

References 9 publications

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“…The use of the classical Radon transform for deconvolution has been proposed before (e.g., [21]). The most well-known version of the classical Radon transform of a function x with domain R 2 is defined as…”

Section: Historical Perspectivementioning

confidence: 99%

Image Deconvolution Using a General Ridgelet and Curvelet Domain

Easley¹,

Healy²,

Berenstein³

2009

SIAM J. Imaging Sci.

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We carry out deconvolution by transforming the data into a new general discrete Radon domain that can handle any assumed boundary conditions for the associated matrix inversion problem. For each associated component (projection), one can then apply deconvolution routines to smaller (and possibly better) conditioned matrix inversion problems than the matrix inversion problem for the entire image. We demonstrate this new scheme by adaptively deconvolving these components using a combination of regularized inversion and wavelet filtering techniques. This procedure allows us to provide image estimates based on a generalized ridgelet frame. We then devise methods for carrying out this scheme locally to provide estimates based on generalized multiscaled ridgelets which are then filtered and combined to form an estimate from a curvelet-like domain. The techniques presented here suggest a whole new paradigm for developing deconvolution algorithms that incorporate leading deconvolution schemes. Various experimental results show that our methods can perform significantly better than standard deconvolution techniques. Introduction.A typical restoration problem can be modeled as the desired image convolved with some type of point spread function. The resulting degraded image is referred to as a blurred image, and the recovery of the original image from the blurred image is called deconvolution. It is well known that such a problem is ill-posed.In this work, we propose a new generalized discrete Radon transform (GDRT) that avoids interpolation and reduces a two-dimensional discrete deconvolution problem into a set of onedimensional discrete inverse problems. A preliminary version of this GDRT was given in [6] and has been extended here to deal with deconvolution problems that can be solved by a variety of inverse problem methods. Besides reducing the complexity for each inverse problem, splitting the image deconvolution problem into a set of smaller-sized matrix inversion problems has other advantages. The matrices for these smaller problems may be better conditioned, and the underlying signals to be estimated tend to be smoother than the corresponding segments extracted from the original image, yielding better estimates. There is also a natural noise filtering when inverting the GDRT. We illustrate these benefits with many examples and, whenever possible, provide a detailed analysis from a numerical linear algebra perspective.We illustrate the usefulness of this new transform method for deconvolution by examining wavelet-based regularization schemes on the associated one-dimensional problems. These

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Section: Historical Perspectivementioning

confidence: 99%

Image Deconvolution Using a General Ridgelet and Curvelet Domain

Easley¹,

Healy²,

Berenstein³

2009

SIAM J. Imaging Sci.

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“…These include blind deconvolution (Shalvi and Weinstein 1990), blind source separation (Tugnait 1997), direction finding (Porat and Friedlander 1991), and speech detection (Nemer et al 2001), all of which can benefit from on-line updates to adapt to changing channel conditions and minimize delay. Image processing also makes frequent use of higher-order moments for modeling non-linear distortions, with applications in deblurring (Xu and Crebbin 1996;Ibrahim et al 1998;Wang et al 2006), noise removal (Kleihorst et al 1997), gamma correction and radial distortion estimation (Farid and Popescu 2001), and steganalysis (Lyu and Farid 2002). Skewness and kurtosis are also commonly used in financial modeling (Samuelson 1970;Harvey and Siddique 2000), where datasets are so large that distributed processing is required.…”

Section: Introductionmentioning

confidence: 99%

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Pébaÿ

Terriberry²,

Kolla³

et al. 2016

Comput Stat

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Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables Dedicated to the Memory of Dr Timothy J. Baker (1948Baker ( -2006 the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

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“…Higher-order statistics have previously been used for various forms of image restoration: noise removal [2], deblurring [3,4], and speckle removal [5]. See also [6,7,8] for general discussions on the use of higher-order statistics in image processing.…”

Section: Introductionmentioning

confidence: 99%

Blind inverse gamma correction

Farid

2001

IEEE Trans. on Image Process.

290

145

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The luminance nonlinearity introduced by many imaging devices can often be described by a simple point-wise operation (gamma correction). This paper presents a technique for blindly estimating the amount of gamma correction in the absence of any calibration information or knowledge of the imaging device. The basic approach exploits the fact that gamma correction introduces specific higher-order correlations in the frequency domain. These correlations can be detected using tools from polyspectral analysis. The amount of gamma correction is then estimated by minimizing these correlations.

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A blind image restoration system using higher-order statistics and Radon transform

Cited by 5 publications

References 9 publications

Image Deconvolution Using a General Ridgelet and Curvelet Domain

Image Deconvolution Using a General Ridgelet and Curvelet Domain

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Blind inverse gamma correction

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