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ForWaRD: FourierWavelet Regularized Deconvolution for IllConditioned Systems
 IEEE Trans. on Signal Processing
, 2002
"... We propose an efficient, hybrid FourierWavelet Regularized Deconvolution (ForWaRD) al gorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's sparse representation of the colored noise i ..."
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Cited by 114 (2 self)
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We propose an efficient, hybrid FourierWavelet Regularized Deconvolution (ForWaRD) al gorithm that performs noise regularization via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the Fourier transform's sparse representation of the colored noise inherent in deconvolution, while the wavelet shrinkage exploits the wavelet do main's sparse representation of piecewise smooth signals and images. We derive the optimal balance between the amount of Fourier and wavelet regularization by optimizing an approxi mate meansquarederror (MSE) metric and find that signals with sparser wavelet representa tions require less Fourier shrinkage. ForWaRD is applicable to all illconditioned deconvolution problems, unlike the purely waveletbased Wavelet Vaguelette Deconvolution (WVD), and its es timate features minimal ringing, unlike purely Fourierbased Wiener deconvolution. We analyze ForWaRD's MSE decay rate as the number of samples increases and demonstrate its improved performance compared to the optimal WVD over a wide range of practical samplelengths.
A WaveletLaplace Variational Technique for Image . . .
 IEEE TRANSACTIONS IN IMAGE PROCESSING
"... We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDEbased techniques involving the GinzburgLandau functional, but using more localized waveletbased methods. We present results for both binary and grayscale images. Comparable speeds are ac ..."
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Cited by 27 (12 self)
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We construct a new variational method for blind deconvolution of images and inpainting, motivated by recent PDEbased techniques involving the GinzburgLandau functional, but using more localized waveletbased methods. We present results for both binary and grayscale images. Comparable speeds are achieved with better sharpness of edges in the reconstruction.
Inverse Problems in Image Processing
, 2003
"... Inverse problems involve estimating parameters or data from inadequate observations; the observations are often noisy and contain incomplete information about the target parameter or data due to physical limitations of the measurement devices. Consequently, solutions to inverse problems are nonuni ..."
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Cited by 2 (2 self)
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Inverse problems involve estimating parameters or data from inadequate observations; the observations are often noisy and contain incomplete information about the target parameter or data due to physical limitations of the measurement devices. Consequently, solutions to inverse problems are nonunique. To pin down a solution, we must exploit the underlying structure of the desired solution set. In this thesis, we formulate novel solutions to three image processing inverse problems: deconvolution, inverse halftoning, and JPEG compression history estimation for color images. Deconvolution aims to extract crisp images from blurry observations. We propose an efficient, hybrid FourierWavelet Regularized Deconvolution (ForWaRD) algorithm that comprises blurring operator inversion followed by noise attenuation via scalar shrinkage in both the Fourier and wavelet domains. The Fourier shrinkage exploits the structure of the colored noise inherent in deconvolution, while the wavelet shrinkage exploits the piecewise smooth structure of realworld signals and images. ForWaRD yields stateoftheart meansquarederror (MSE) performance in practice. Further, for certain problems, ForWaRD guarantees an optimal rate of MSE decay with increasing resolution. Halftoning is a
WInliD: Waveletbased Inverse Halftoning via Deconvolution
, 2002
"... We propose the Waveletbased Inverse Halftoning via Deconvolution (WInliD) algorithm to perform inverse halftoning of errordiffused halftones. WInliD is motivated by our realization that inverse halftoning can be formulated as a deconvolution problem under Kite et al.'s linear approximation ..."
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We propose the Waveletbased Inverse Halftoning via Deconvolution (WInliD) algorithm to perform inverse halftoning of errordiffused halftones. WInliD is motivated by our realization that inverse halftoning can be formulated as a deconvolution problem under Kite et al.'s linear approximation model for error diffusion halftoning. Under the linear model, the errordiffused halftone comprises the original grayscale image blurred by a convolution operator and colored noise; the convolution operator and noise coloring are determined by the error diffusion tech nique. WInliD performs inverse halftoning by first inverting the modelspecified convolution operator and then attenuating the residual noise using scalar waveletdomain shrinkage. Since WInliD is modelbased, it is easily adapted to different error diffusion halftoning techniques. Using
Focus recovery for extended depthoffield mobile imaging systems
"... We describe a solution for image restoration in a computational camera known as an extended depth of field (EDOF) system. The speciallydesigned optics produce point spread functions that are roughly invariant with object distance in a range. However, this invariance involves a tradeoff with the pe ..."
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We describe a solution for image restoration in a computational camera known as an extended depth of field (EDOF) system. The speciallydesigned optics produce point spread functions that are roughly invariant with object distance in a range. However, this invariance involves a tradeoff with the peak sharpness of the lens. The lens blur is a function of lens fieldheight, and the imaging sensor introduces signaldependent noise. In this context, the principal contributions of this paper are: a) the modeling of the EDOF focus recovery problem; and b) the adaptive EDOF focus recovery approach, operating in signaldependent noise. The focus recovery solution is adaptive to complexities of an EDOF imaging system, and performs a joint deblurring and noise suppression. It also adapts to imaging conditions by accounting for the state of the sensor (e.g., lowlight conditions).