Variational Dirichlet Blur Kernel Estimation

Analysis and Application of Matrix-Form Neural Networks for Fast Matrix-Variable Convex Optimization

Matrix-variable optimization is a generalization of vector-variable optimization and has been found to have many important applications. To reduce computation time and storage requirement, this article presents two matrix-form recurrent neural networks (RNNs), one continuous-time model and another discrete-time model, for solving matrix-variable optimization problems with linear constraints. The two proposed matrix-form RNNs have low complexity and are suitable for parallel implementation in terms of matrix state space. The proposed continuous-time matrix-form RNN can significantly generalize existing continuous-time vector-form RNN. The proposed discrete-time matrix-form RNN can be effectively used in blind image restoration, where the storage requirement and computational cost are largely reduced. Theoretically, the two proposed matrix-form RNNs are guaranteed to be globally convergent to the optimal solution under mild conditions. Computed results show that the proposed matrix-form RNN-based algorithm is superior to related vector-form RNN and matrix-form RNN-based algorithms, in terms of computation time.

On the Comparisons of Decorrelation Approaches for Non-Gaussian Neutral Vector Variables

As a typical non-Gaussian vector variable, a neutral vector variable contains nonnegative elements only, and its l₁ -norm equals one. In addition, its neutral properties make it significantly different from the commonly studied vector variables (e.g., the Gaussian vector variables). Due to the aforementioned properties, the conventionally applied linear transformation approaches [e.g., principal component analysis (PCA) and independent component analysis (ICA)] are not suitable for neutral vector variables, as PCA cannot transform a neutral vector variable, which is highly negatively correlated, into a set of mutually independent scalar variables and ICA cannot preserve the bounded property after transformation. In recent work, we proposed an efficient nonlinear transformation approach, i.e., the parallel nonlinear transformation (PNT), for decorrelating neutral vector variables. In this article, we extensively compare PNT with PCA and ICA through both theoretical analysis and experimental evaluations. The results of our investigations demonstrate the superiority of PNT for decorrelating the neutral vector variables.

A Deconvolutional Deblurring Algorithm Based on Dual-Channel Images

Aiming at the motion blur restoration of large-scale dual-channel space-variant images, this paper proposes a dual-channel image deblurring method based on the idea of block aggregation, by studying imaging principles and existing algorithms. The study first analyzed the model of dual-channel space-variant imaging, reconstructed the kernel estimation process using the side prior information from the correlation of the two-channel images, and then used a clustering algorithm to classify kernels and restore the images. In the kernel estimation process, the study proposed two kinds of regularization terms. One is based on image correlation, and the other is based on the information from another channel input. In the image restoration process, the mean-shift clustering algorithm was used to calculate the block image kernel weights and reconstruct the final restored image according to the weights. As the experimental section shows, the restoration effect of this algorithm was better than that of the other compared algorithms.

A Deconvolutional Deblurring Algorithm Based on Short- and Long-Exposure Images

An iterative image restoration algorithm, directed at the image deblurring problem and based on the concept of long- and short-exposure deblurring, was proposed under the image deconvolution framework by investigating the imaging principle and existing algorithms, thus realizing the restoration of degraded images. The effective priori side information provided by the short-exposure image was utilized to improve the accuracy of kernel estimation, and then increased the effect of image restoration. For the kernel estimation, a priori filtering non-dimensional Gaussianity measure (BID-PFNGM) regularization term was raised, and the fidelity term was corrected using short-exposure image information, thus improving the kernel estimation accuracy. For the image restoration, a P norm-constrained relative gradient regularization term constraint model was put forward, and the restoration result realizing both image edge preservation and texture restoration effects was acquired through the further processing of the model results. The experimental results prove that, in comparison with other algorithms, the proposed algorithm has a better restoration effect.

Effective Blind Image Deblurring Using Matrix-Variable Optimization

Blind image deblurring has been a challenging issue due to the unknown blur and computation problem. Recently, the matrix-variable optimization method successfully demonstrates its potential advantages in computation. This paper proposes an effective matrix-variable optimization method for blind image deblurring. Blur kernel matrix is exactly decomposed by a direct SVD technique. The blur kernel and original image are well estimated by minimizing a matrix-variable optimization problem with blur kernel constraints. A matrix-type alternative iterative algorithm is proposed to solve the matrix-variable optimization problem. Finally, experimental results show that the proposed blind image deblurring method is much superior to the state-of-the-art blind image deblurring algorithms in terms of image quality and computation time.

Parameter-free Gaussian PSF Model for Extended Depth of Field in Brightfield Microscopy

Due to their limited depth of field, conventional brightfield microscopes cannot image thick specimens entirely in focus. A common way to obtain an all-in-focus image is to acquire a z-stack of images by optically sectioning the specimen and then apply a multi-focus fusion method. Unfortunately, for undersampled image stacks, fusion methods cannot remove the blur in regions where the in-focus position is between two optical sections. In this work, we propose a parameter-free Gaussian PSF model in which the all-in-focus image together with both the depth map and sampling distances in image plane are estimated from the image sequence automatically, without knowledge on the z-stack acquisition. In a maximum a posteriori framework, an iteratively reweighted least squares method is used to estimate the image and an adaptive scaled gradient descent method is utilized to estimate the depth map and sampling distances efficiently. Experiments on synthetic and real data demonstrate that the proposed method outperforms the current state-of-the-art, mitigating fusion artifacts and recovering sharper edges.