In this paper, we propose a fast fixed point algorithm and apply it to total variation (TV) deblurring and segmentation. The TV-based models can be written in the form of a general minimization problem. The novel method is derived from the idea of establishing the relation between solutions of the general minimization problem and new variables, which can be obtained by a fixed point algorithm efficiently. Under gentle conditions it provides a platform to develop efficient numerical algorithms for various image processing tasks. We then specialize this fixed point methodology to the TV-based image deblurring and segmentation models, and the resulting algorithms are compared with the split Bregman method, which is a strong contender for the state-of-the-art algorithms. Numerical experiments demonstrate that the algorithm proposed here performs favorably.

We present a computer-aided diagnosis system (CADx) for the automatic categorization of solid, part-solid and non-solid nodules in pulmonary computerized tomography images using a Convolutional Neural Network (CNN). Provided with only a two-dimensional region of interest (ROI) surrounding each nodule, our CNN automatically reasons from image context to discover informative computational features. As a result, no image segmentation processing is needed for further analysis of nodule attenuation, allowing our system to avoid potential errors caused by inaccurate image processing. We implemented two computerized texture analysis schemes, classification and regression, to automatically categorize solid, part-solid and non-solid nodules in CT scans, with hierarchical features in each case learned directly by the CNN model. To show the effectiveness of our CNN-based CADx, an established method based on histogram analysis (HIST) was implemented for comparison. The experimental results show significant performance improvement by the CNN model over HIST in both classification and regression tasks, yielding nodule classification and rating performance concordant with those of practicing radiologists. Adoption of CNN-based CADx systems may reduce the inter-observer variation among screening radiologists and provide a quantitative reference for further nodule analysis.

The total variation (TV) model with a fidelity term of the generalized Kullback-Leibler (KL) divergence is a classical method for Poissonian image deblurring. In this paper, we propose a new TV-KL model with a spatially dependent regularization parameter. This model is able to preserve small details of images while homogeneous regions still remain sufficiently smooth. The automated selection of the regularization parameter is based on the local discrepancy function. The corresponding minimization problem with a spatially adapted regularization parameter can be solved efficiently by the split Bregman method. Numerical experiments demonstrate that the proposed algorithm has the potential to enhance regions of images containing detail and remove Poisson noise simultaneously, which leads to an improvement in the signal-to-noise ratio and the mean absolute error for deblurring results.

In digital images, the performance of optical aberration is a multivariate degradation, where the spectral of the scene, the lens imperfections, and the field of view together contribute to the results. Besides eliminating it at the hardware level, the post-processing system, which utilizes various prior information, is significant for correction. However, due to the content differences among priors, the pipeline that aligns these factors shows limited efficiency and unoptimized restoration.Here, we propose a prior quantization model to correct the optical aberrations in image processing systems. To integrate these messages, we encode various priors into a latent space and quantify them by the learnable codebooks. After quantization, the prior codes are fused with the image restoration branch to realize targeted optical aberration correction. Comprehensive experiments demonstrate the flexibility of the proposed method and validate its potential to accomplish targeted restoration for a specific camera. Furthermore, our model promises to analyze the correlation between the various priors and the optical aberration of devices, which is helpful for joint soft-hardware design.

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