In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes edge preserving measures or frame-analysis potentials commonly used in image processing. As shown by our asymptotic results, the ℓ 2 − ℓ 0 penalties we consider may be employed to provide approximate solutions to ℓ 0penalized optimization problems. One of the advantages of the proposed approach is that it allows us to derive an efficient Majorize-Minimize subspace algorithm. The convergence of the algorithm is investigated by using recent results in nonconvex optimization. The fast convergence properties of the proposed optimization method are illustrated through image processing examples. In particular, its effectiveness is demonstrated on several data recovery problems. * A preliminary version of this work has appeared in [18].
The Poisson-Gaussian model can accurately describe the noise present in a number of imaging systems. However most existing restoration methods rely on approximations of the Poisson-Gaussian noise statistics. We propose a convex optimization strategy for the reconstruction of images degraded by a linear operator and corrupted with a mixed Poisson-Gaussian noise. The originality of our approach consists of considering the exact, mixed continuous-discrete model corresponding to the data statistics. After establishing the Lipschitz differentiability and convexity of the Poisson-Gaussian neg-log-likelihood, we derive a primal-dual iterative scheme for minimizing the associated penalized criterion. The proposed method is applicable to a large choice of convex penalty terms. The robustness of our scheme allows us to handle computational difficulties due to infinite sums arising from the computation of the gradient of the criterion. We propose finite bounds for these sums, that are dependent on the current image estimate, and thus adapted to each iteration of our algorithm. The proposed approach is validated on image restoration examples. Then, the exact data fidelity term is used as a reference for studying some of its various approximations. We show that in a variational framework the Shifted Poisson and Exponential approximations lead to very good restoration results.
International audienceThe problem of estimating the parameters of a Poisson-Gaussian model from experimental data has recently raised much interest in various applications, for instance in confocal fluorescence microscopy. In this context, a field of independent random variables is observed, which is varying both in time and space. Each variable is a sum of two components, one following a Poisson and the other a Gaussian distribution. In this paper, a general formulation is considered where the associated Poisson process is nonstationary in space and also exhibits an exponential decay in time, whereas the Gaussian component corresponds to a stationary white noise with arbitrary mean. To solve the considered parametric estimation problem, we follow an iterative Expectation-Maximization (EM) approach. The parameter update equations involve deriving finite approximation of infinite sums. Expressions for the maximum error incurred in the process are also given. Since the problem is non-convex, we pay attention to the EM initialization, using a moment-based method where recent optimization tools come into play. We carry out a performance analysis by computing the Cramer-Rao bounds on the estimated variables. The practical performance of the proposed estimation procedure is illustrated on both synthetic data and real fluorescence macroscopy image sequences. The algorithm is shown to provide reliable estimates of the mean/variance of the Gaussian noise and of the scale parameter of the Poisson component, as well as of its exponential decay rate. In particular, the mean estimate of the Poisson component can be interpreted as a good-quality denoised version of the data
A Poisson-Gaussian model accurately describes the noise present in many imaging systems such as CCD cameras or fluorescence microscopy. However most existing restoration strategies rely on approximations of the Poisson-Gaussian noise statistics. We propose a convex optimization algorithm for the reconstruction of signals degraded by a linear operator and corrupted with mixed Poisson-Gaussian noise. The originality of our approach consists of considering the exact continuous-discrete model corresponding to the data statistics. After establishing the Lipschitz differentiability of the Poisson-Gaussian log-likelihood, we derive a primal-dual iterative scheme for minimizing the associated penalized criterion. The proposed method is applicable to a large choice of penalty terms. The robustness of our scheme allows us to handle computational difficulties due to infinite sums arising from the computation of the gradient of the criterion. The proposed approach is validated on image restoration examples.
In this paper, we present a new fully automatic approach for noise parameter estimation in the context of fluorescence imaging systems. In particular, we address the problem of Poisson-Gaussian noise modeling in the nonstationary case. In microscopy practice, the nonstationarity is due to the photobleaching effect. The proposed method consists of an adequate moment based initialization followed by Expectation-Maximization iterations. This approach is shown to provide reliable estimates of the mean and the variance of the Gaussian noise and of the scale parameter of Poisson noise, as well as of the photobleaching rates. The algorithm performance is demonstrated on both synthetic and real macro confocal laser scanning microscope image sequences.
In this paper, we consider a class of differentiable criteria for sparse image recovery problems. The regularization is applied to a linear transform of the target image. As special cases, it includes edge preserving measures or frame analysis potentials. As shown by our asymptotic results, the considered 2 − 0 penalties may be employed to approximate solutions to 0 penalized optimization problems. One of the advantages of the approach is that it allows us to derive an efficient Majorize-Minimize Memory Gradient algorithm. The fast convergence properties of the proposed optimization algorithm are illustrated through image restoration examples.
Localizing instrument parts in video-assisted surgeries is an attractive and open computer vision problem. A working algorithm would immediately find applications in computer-aided interventions in the operating theater. Knowing the location of tool parts could help virtually augment visual faculty of surgeons, assess skills of novice surgeons, and increase autonomy of surgical robots. A surgical tool varies in appearance due to articulation, viewpoint changes, and noise. We introduce a new method for detection and pose estimation of multiple non-rigid and robotic tools in surgical videos. The method uses a rigidly structured, bipartite model of end-effector and shaft parts that consistently encode diverse, pose-specific appearance mixtures of the tool. This rigid part mixtures model then jointly explains the evolving tool structure by switching between mixture components. Rigidly capturing end-effector appearance allows explicit transfer of keypoint meta-data of the detected components for full 2D pose estimation. The detector can as well delineate precise skeleton of the end-effector by transferring additional keypoints. To this end, we propose effective procedure for learning such rigid mixtures from videos and for pooling the modeled shaft part that undergoes frequent truncation at the border of the imaged scene. Notably, extensive diagnostic experiments inform that feature regularization is a key to fine-tune the model in the presence of inherent appearance bias in videos. Experiments further illustrate that estimation of end-effector pose improves upon including the shaft part in the model. We then evaluate our approach on publicly available datasets of in-vivo sequences of non-rigid tools and demonstrate state-of-the-art results.
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