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A graph cut algorithm for generalized image deconvolution
 In ICCV
, 2005
"... The goal of deconvolution is to recover an image x from its convolution with a known blurring function. This is equivalent to inverting the linear system y = Hx. In this paper we consider the generalized problem where the system matrix H is an arbitrary nonnegative matrix. Linear inverse problems c ..."
Abstract

Cited by 13 (2 self)
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The goal of deconvolution is to recover an image x from its convolution with a known blurring function. This is equivalent to inverting the linear system y = Hx. In this paper we consider the generalized problem where the system matrix H is an arbitrary nonnegative matrix. Linear inverse problems can be solved by adding a regularization term to impose spatial smoothness. To avoid oversmoothing, the regularization term must preserve discontinuities; this results in a particularly challenging energy minimization problem. Where H is diagonal, as occurs in image denoising, the energy function can be solved by techniques such as graph cuts, which have proven to be very effective for problems in early vision. When H is nondiagonal, however, the data cost for a pixel to have a intensity depends on the hypothesized intensities of nearby pixels, so existing graph cut methods cannot be applied. This paper shows how to use graph cuts to obtain a discontinuitypreserving solution to a linear inverse system with an arbitrary nonnegative system matrix. We use a dynamically chosen approximation to the energy which can be minimized by graph cuts; minimizing this approximation also decreases the original energy. Experimental results are shown for MRI reconstruction from fourier data. 1. Generalized Image Deconvolution The goal of image deconvolution is to recover an image x from its convolution with a known blurring function h. This is equivalent to solving the linear inverse problem [1] y = Hx (1) for x given y, where H is the convolution matrix corresponding to h. In this paper we consider the generalized image deconvolution problem, where H is an arbitrary nonnegative matrix. This generalization is motivated by an important problem in medical imaging, namely the reconstruction of MRI images from fourier data. We will discuss this problem in more detail in section 5.1; for the moment, we