Computed tomography noise reduction based on total variation minimization and morphological component analysis

X-ray Computed Tomography (CT) scans, while useful, emit harmful radiation which is why low-dose image acquisition is desired. However, noise corruption in these cases is a difficult obstacle. CT image denoising is a challenging topic because of the difficulty in modeling noise. In this study, we propose taking an image decomposition approach to removing noise from low-dose CT images. We model the image as the superposition of a structure layer and a noise layer. Total Variation (TV) minimization is used to learn two dictionaries to represent each layer independently, and sparse coding is used to separate them. Finally, an iterative post-processing stage is introduced that uses image-adapted curvelet dictionaries to recover blurred edges. Our results demonstrate that image separation is a viable alternative to the classic K-SVD denoising method.

Computed tomography noise reduction based on total variation minimization and morphological component analysis

X-ray Computed Tomography (CT) scans, while useful, emit harmful radiation which is why low-dose image acquisition is desired. However, noise corruption in these cases is a difficult obstacle. CT image denoising is a challenging topic because of the difficulty in modeling noise. In this study, we propose taking an image decomposition approach to removing noise from low-dose CT images. We model the image as the superposition of a structure layer and a noise layer. Total Variation (TV) minimization is used to learn two dictionaries to represent each layer independently, and sparse coding is used to separate them. Finally, an iterative post-processing stage is introduced that uses image-adapted curvelet dictionaries to recover blurred edges. Our results demonstrate that image separation is a viable alternative to the classic K-SVD denoising method.

On the convergence of recursive SURE for total variation minimization

Recently, total variation (TV) regularization has become a standard technique for image recovery. The mean squared error (MSE) of the reconstruction can be reliably estimated by Stein’s unbiased risk estimate (SURE). In this work, we develop two recursive evaluations of SURE, based on Chambolle’s projection method (CPM) for TV denoising and alternating direction method of multipliers (ADMM) for TV deconvolution, respectively. In particular, from the proximal point perspective, we provide the convergence analysis for both iterative schemes and the corresponding Jacobian recursions, in terms of the solution distance, from which follows the convergence of noise evolution of Monte-Carlo simulation in practical computations. The theoretical analysis is supported by numerical examples.

Approximation of the Mumford–Shah functional by phase fields of bounded variation

In this paper, we introduce a new phase field approximation of the Mumford–Shah functional similar to the well-known one from Ambrosio and Tortorelli. However, in our setting the phase field is allowed to be a function of bounded variation, instead of an [Formula: see text]-function. In the context of image segmentation, we also show how this new approximation can be used for numerical computations, which contains a total variation minimization of the phase field variable, as it appears in many problems of image processing. A comparison to the classical Ambrosio–Tortorelli approximation, where the phase field is an [Formula: see text]-function, shows that the new model leads to sharper phase fields.