Image sequence filtering in quantum-limited noise with applications to low-dose fluoroscopy

Chan, Cheuk L.; Katsaggelos, Aggelos K.; Sahakian, Alan V.

doi:10.1109/42.241890

Cited by 79 publications

(42 citation statements)

References 34 publications

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“…and video coding, and many others [35,13,46,2,32]. We focus on the most common image degradation model where the observed data g ∈ R q are related to the underlying image f ∈ R p as (1.1) g = Hf + n, where n represents the noise and H is a q×p matrix representing, for instance, optical blurring, distortion wavelets in seismic imaging and nondestructive evaluation, a Radon transform in Xray tomography, and a Fourier transform in diffraction tomography.…”

mentioning

confidence: 99%

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Nikolova¹,

Ng²,

Zhang³

et al. 2008

SIAM J. Imaging Sci.

180

171

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Abstract. We consider the restoration of piecewise constant images where the number of the regions and their values are not fixed in advance, with a good difference of piecewise constant values between neighboring regions, from noisy data obtained at the output of a linear operator (e.g., a blurring kernel or a Radon transform). Thus we also address the generic problem of unsupervised segmentation in the context of linear inverse problems. The segmentation and the restoration tasks are solved jointly by minimizing an objective function (an energy) composed of a quadratic data-fidelity term and a nonsmooth nonconvex regularization term. The pertinence of such an energy is ensured by the analytical properties of its minimizers. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonsmooth nonconvex minimization. Indeed, the existing methods are unsatisfactory since they (implicitly or explicitly) involve a smooth approximation of the regularization term and often get stuck in shallow local minima. The goal of this paper is to design a method that efficiently handles the nonsmooth nonconvex minimization. More precisely, we propose a continuation method where one tracks the minimizers along a sequence of approximate nonsmooth energies {Jε}, the first of which being strictly convex and the last one the original energy to minimize. Knowing the importance of the nonsmoothness of the regularization term for the segmentation task, each Jε is nonsmooth and is expressed as the sum of an 1 regularization term and a smooth nonconvex function. Furthermore, the local minimization of each Jε is reformulated as the minimization of a smooth function subject to a set of linear constraints. The latter problem is solved by the modified primal-dual interior point method, which guarantees the descent direction at each step. Experimental results are presented and show the effectiveness and the efficiency of the proposed method. Comparison with simulated annealing methods further shows the advantage of our method.

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mentioning

confidence: 99%

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Nikolova¹,

Ng²,

Zhang³

et al. 2008

SIAM J. Imaging Sci.

180

171

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“…This problem plays an important role in medical sciences, biological engineering and other areas of science and engineering [1,4,31]. The most common image degradation model can be represented by the following system:…”

Section: Introductionmentioning

confidence: 99%

Smoothing Nonlinear Conjugate Gradient Method for Image Restoration Using Nonsmooth Nonconvex Minimization

Chen¹,

Zhou²

2010

SIAM J. Imaging Sci.

118

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Image restoration problems are often converted into large-scale, nonsmooth and nonconvex optimization problems. Most existing minimization methods are not efficient for solving such problems. It is well-known that nonlinear conjugate gradient methods are preferred to solve large-scale smooth optimization problems due to their simplicity, low storage, practical computation efficiency and nice convergence properties. In this paper, we propose a smoothing nonlinear conjugate gradient method where an intelligent scheme is used to update the smoothing parameter at each iteration and guarantees that any accumulation point of a sequence generated by this method is a Clarke stationary point of the nonsmooth and nonconvex optimization problem. Moreover, we present a class of smoothing functions and show their approximation properties. This method is easy to implement without adding any new variables.

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“…In the case of very low count situations (≤ 1 photons in average), the more sophisticated Fisz transform allows one to better stabilize Poisson noise [7], [8]. Finally, local estimation of image-dependent noise statistics (assumed to be locally Gaussian) has also been investigated, especially in the case of adaptive Wiener filtering [9]- [11].…”

Section: Introductionmentioning

confidence: 99%

“…When temporal coherence is exploited, it is usually recommended to consider a motion estimation/compensation stage as proposed for video denoising [14]- [17] and, for instance, for low-dose fluoroscopy image sequence filtering [11]. This is especially true for real-time imaging applications.…”

Section: Introductionmentioning

confidence: 99%

Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences

Boulanger

Kervrann

Bouthémy

et al. 2010

IEEE Trans. Med. Imaging

268

262

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Abstract-We present a non-parametric regression method for denoising 3D image sequences acquired via fluorescence microscopy. The proposed method exploits the redundancy of the 3D+time information to improve the signal-to-noise ratio of images corrupted by PoissonGaussian noise. A variance stabilization transform is first applied to the image-data to remove the dependence between the mean and variance of intensity values. This preprocessing requires the knowledge of parameters related to the acquisition system, also estimated in our approach. In a second step, we propose an original statistical patchbased framework for noise reduction and preservation of space-time discontinuities. In our study, discontinuities are related to small moving spots with high velocity observed in fluorescence video-microscopy. The idea is to minimize an objective non-local energy functional involving spatiotemporal image patches. The minimizer has a simple form and is defined as the weighted average of input data taken in spatially-varying neighborhoods. The size of each neighborhood is optimized to improve the performance of the pointwise estimator. The performance of the algorithm (which requires no motion estimation) is then evaluated on both synthetic and real image sequences using qualitative and quantitative criteria.Index Terms-Video-microscopy, fluorescence, image sequence denoising, patch-based approach, Poisson noise, variance stabilization, adaptive estimation, energy minimization.

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Image sequence filtering in quantum-limited noise with applications to low-dose fluoroscopy

Cited by 79 publications

References 34 publications

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

Smoothing Nonlinear Conjugate Gradient Method for Image Restoration Using Nonsmooth Nonconvex Minimization

Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences

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