Efficient blind blur identification using discrete periodic Radon transform

Lun, Daniel Pak-Kong; Hsung, Tai-Chiu; Dong, Feng

doi:10.1109/isimp.2001.925336

Cited by 5 publications

(2 citation statements)

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“…As a consequence, after applying deconvolution methods the standard algorithms for computing the Radon transform of a blurred image s can cause severe artifacts in the estimated image, due to the interpolations needed to approximate the Radon transform. In an effort to overcome this limitation, discrete variants of the Radon transform have been proposed in [1] and [28]. In [20] it was shown that under periodic boundary conditions the convolution property holds for the discrete Radon transform known as periodic Radon transform, which is a special case of the p-adic Radon transform (p = 2).…”

Section: Historical Perspectivementioning

confidence: 99%

“…In [20] it was shown that under periodic boundary conditions the convolution property holds for the discrete Radon transform known as periodic Radon transform, which is a special case of the p-adic Radon transform (p = 2). The method of doing blind deconvolution along the projections of the periodic Radon transform was tested in [28].…”

Section: Historical Perspectivementioning

confidence: 99%

See 1 more Smart Citation

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%

Section: Historical Perspectivementioning

confidence: 99%