20-06-2011, 09:48 AM
Submitted By
Saurabh Singhal
Ramandeep Singh
[attachment=14110]
ABSTRACT
Classical linear image restoration techniques assume that the linear shift invariant blur, also known as the point - spread function (PSF), is known prior to restoration. In many practical situations, however, the PSF is unknown and the problem of image restoration involves the simultaneous identification of the true image and PSF from the degraded observation. Such a process is referred to as blind deconvolution. This paper presents a novel blind deconvolution method for image restoration. The method is flexible for incorporating different constraints on the true image. An example of the method is given for situations in which the imaged scene consists of a finite support object against a uniformly grey back- ground. The only information required are the nonnegativity of the true image and the support size of the original object. For situations in which the exact object support is unknown, a novel support-finding algorithm is proposed.
1. INTRODUCTION
Image restoration refers to the task of recovering an image from a degraded observation. Although classical linear image restoration techniques have been thoroughly studied, the more difficult problem of blind image restoration has numerous research possibilities.
In applications such as artificial satellite imaging, remote sensing, and medical imaging, improved image quality is often costly or physically impossible to obtain. In addition, little is known about the image to be restored, and it is often difficult to calculate or measure the PSF explicitly. The problem of simultaneously estimating the PSF (or its inverse) and restoring an unknown image is called
blind deconvolution. The goal is to obtain a shifted scaled version of the original image. Theoretically, the scale and shift of an image are not recoverable in general by blind deconvolution algorithms.
Initial research into blind deconvolution of images assumed that the degradation of the image resulted from linear camera motion or an out-of- focus camera lens. Based on these models a parametric form for the PSF was derived, and the parameter values were estimated using the frequency domain nulls of the degraded image. The major drawback of existing blind deconvolution methods for images is that they suffer from poor convergence properties.
This paper presents a novel technique for the class of non-parametric deterministic image constraints methods that overcomes the limitations of existing techniques. The general method involves the iterative minimization of a convex cost function. The image is restored by filtering the blurred image to produce an image estimate which is restricted to lie on a convex set representing the known deterministic constraints of the true image. The approach can incorporate a variety of constraints on the image such as pixel amplitude bounds, support, maximum energy, and smoothness, among others.
This paper focusses the particular situation in which an object of finite extent is imaged against a uniformly grey background. The edges of the object are assumed to be completely or almost completely included within the observed frame. This often occurs in applications such as astronomy and medical imaging. Statistical knowledge of the original image or a parametric model of the PSF are not needed. The only information required for restoration is the nonnegativity of the true image, and support size of the original object. This particular algorithm, referred to as the Nonnegativity and Support constraints Recursive Inverse Filtering (NAS-RIF) technique , involves numerically minimizing a convex cost function. All other methods incorporate the minimization of nonconvex cost
functions ,the advantage of the proposed NAS-RIF technique is that convergence to the global minimum is guaranteed, even in the presence of noise. In addition, the proposed technique shows faster convergence speed than existing iterative techniques and does not require heavy memory requirements. The superior performance of the NAS-RIF algorithm is demonstrated by computer simulations and comparisons with existing methods of its class. The proposed technique belongs to the class of nonparametric finite support blind image restoration
methods. The degradation process is assumed to be represented by the following linear model :
g(x,y) = f(x,y) * h(x,y) + n(x,y)
where f(x; y) is the true image, h(x; y) is the PSF, n(x; y) is the additive noise, g(x; y) is the degraded image, (x; y) is the discrete pixel coordinate, and repr-
esents two-dimension linear convolution. The true image is required to be nonnegative with known finite support (the support is defined as the smallest rectangle containing the entire object). In applications such as astronomy, this information is sometimes available. In our method, it can be estimated using a novel technique introduced in section 3. The assumption our algorithm makes about the blur is that its inverse exists.
2. THE PROPOSED METHOD
2.1 The Blind Deconvolution Approach
The proposed NAS-RIF technique consists of a variable FIR filter u(x; y) with the blurred image g(x; y) as input. The output of this filter represents an estimate of the true image ^ f(x; y). This estimate is passed through a nonlinear filter which uses a non-expansive mapping to project the estimated image into the space representing the known characteristics of the true image.
Saurabh Singhal
Ramandeep Singh
[attachment=14110]
ABSTRACT
Classical linear image restoration techniques assume that the linear shift invariant blur, also known as the point - spread function (PSF), is known prior to restoration. In many practical situations, however, the PSF is unknown and the problem of image restoration involves the simultaneous identification of the true image and PSF from the degraded observation. Such a process is referred to as blind deconvolution. This paper presents a novel blind deconvolution method for image restoration. The method is flexible for incorporating different constraints on the true image. An example of the method is given for situations in which the imaged scene consists of a finite support object against a uniformly grey back- ground. The only information required are the nonnegativity of the true image and the support size of the original object. For situations in which the exact object support is unknown, a novel support-finding algorithm is proposed.
1. INTRODUCTION
Image restoration refers to the task of recovering an image from a degraded observation. Although classical linear image restoration techniques have been thoroughly studied, the more difficult problem of blind image restoration has numerous research possibilities.
In applications such as artificial satellite imaging, remote sensing, and medical imaging, improved image quality is often costly or physically impossible to obtain. In addition, little is known about the image to be restored, and it is often difficult to calculate or measure the PSF explicitly. The problem of simultaneously estimating the PSF (or its inverse) and restoring an unknown image is called
blind deconvolution. The goal is to obtain a shifted scaled version of the original image. Theoretically, the scale and shift of an image are not recoverable in general by blind deconvolution algorithms.
Initial research into blind deconvolution of images assumed that the degradation of the image resulted from linear camera motion or an out-of- focus camera lens. Based on these models a parametric form for the PSF was derived, and the parameter values were estimated using the frequency domain nulls of the degraded image. The major drawback of existing blind deconvolution methods for images is that they suffer from poor convergence properties.
This paper presents a novel technique for the class of non-parametric deterministic image constraints methods that overcomes the limitations of existing techniques. The general method involves the iterative minimization of a convex cost function. The image is restored by filtering the blurred image to produce an image estimate which is restricted to lie on a convex set representing the known deterministic constraints of the true image. The approach can incorporate a variety of constraints on the image such as pixel amplitude bounds, support, maximum energy, and smoothness, among others.
This paper focusses the particular situation in which an object of finite extent is imaged against a uniformly grey background. The edges of the object are assumed to be completely or almost completely included within the observed frame. This often occurs in applications such as astronomy and medical imaging. Statistical knowledge of the original image or a parametric model of the PSF are not needed. The only information required for restoration is the nonnegativity of the true image, and support size of the original object. This particular algorithm, referred to as the Nonnegativity and Support constraints Recursive Inverse Filtering (NAS-RIF) technique , involves numerically minimizing a convex cost function. All other methods incorporate the minimization of nonconvex cost
functions ,the advantage of the proposed NAS-RIF technique is that convergence to the global minimum is guaranteed, even in the presence of noise. In addition, the proposed technique shows faster convergence speed than existing iterative techniques and does not require heavy memory requirements. The superior performance of the NAS-RIF algorithm is demonstrated by computer simulations and comparisons with existing methods of its class. The proposed technique belongs to the class of nonparametric finite support blind image restoration
methods. The degradation process is assumed to be represented by the following linear model :
g(x,y) = f(x,y) * h(x,y) + n(x,y)
where f(x; y) is the true image, h(x; y) is the PSF, n(x; y) is the additive noise, g(x; y) is the degraded image, (x; y) is the discrete pixel coordinate, and repr-
esents two-dimension linear convolution. The true image is required to be nonnegative with known finite support (the support is defined as the smallest rectangle containing the entire object). In applications such as astronomy, this information is sometimes available. In our method, it can be estimated using a novel technique introduced in section 3. The assumption our algorithm makes about the blur is that its inverse exists.
2. THE PROPOSED METHOD
2.1 The Blind Deconvolution Approach
The proposed NAS-RIF technique consists of a variable FIR filter u(x; y) with the blurred image g(x; y) as input. The output of this filter represents an estimate of the true image ^ f(x; y). This estimate is passed through a nonlinear filter which uses a non-expansive mapping to project the estimated image into the space representing the known characteristics of the true image.