Qiegen Liu

Adaptive Dictionary Learning in Sparse Gradient Domain for Image Recovery

Image recovery from undersampled data has always been challenging due to its implicit ill-posed nature but becomes fascinating with the emerging compressed sensing (CS) theory. This paper proposes a novel gradient based dictionary learning method for image recovery, which effectively integrates the popular total variation (TV) and dictionary learning technique into the same framework. Specifically, we first train dictionaries from the horizontal and vertical gradients of the image and then reconstruct the desired image using the sparse representations of both derivatives. The proposed method enables local features in the gradient images to be captured effectively, and can be viewed as an adaptive extension of the TV regularization. The results of various experiments on MR images consistently demonstrate that the proposed algorithm efficiently recovers images and presents advantages over the current leading CS reconstruction approaches.

Highly Undersampled Magnetic Resonance Image Reconstruction Using Two-Level Bregman Method With Dictionary Updating

In recent years Bregman iterative method (or related augmented Lagrangian method) has shown to be an efficient optimization technique for various inverse problems. In this paper, we propose a two-level Bregman Method with dictionary updating for highly undersampled magnetic resonance (MR) image reconstruction. The outer-level Bregman iterative procedure enforces the sampled k-space data constraints, while the inner-level Bregman method devotes to updating dictionary and sparse representation of small overlapping image patches, emphasizing local structure adaptively. Modified sparse coding stage and simple dictionary updating stage applied in the inner minimization make the whole algorithm converge in a relatively small number of iterations, and enable accurate MR image reconstruction from highly undersampled k-space data. Experimental results on both simulated MR images and real MR data consistently demonstrate that the proposed algorithm can efficiently reconstruct MR images and present advantages over the current state-of-the-art reconstruction approach.

Augmented Lagrangian based Sparse Representation Method with Dictionary Updating for Image Deblurring

This paper presents an efficient alternating direction method with patch-based dictionary updating, ADMDU-DEB, for sparse representation regularization framework of image deblurring. The main idea of the proposed method is to reformulate the variational problem as a linear equality constrained problem and then minimize its augmented Lagrangian function. The alternating direction method decouples the minimization by alternately iterating the pixel-based regularization and the patch-based sparse representation. Typically, accelerated sparse coding and simple dictionary updating applied in the sparse representation stage enable the whole algorithm to converge at a relatively small number of iterations. Additionally, the approach is readily extended to solve the same kind of variational problem with a nonnegativity constraint. Experimental results on benchmark test images consistently validate the superiority of the proposed approach and demonstrate that it achieves very competitive deblurring performance, co...

PANDA- T1ρ: Integrating principal component analysis and dictionary learning for fast T1ρ mapping

Long scanning time greatly hinders the widespread application of spin‐lattice relaxation in rotating frame ( T1ρ ) in clinics. In this study, a novel method is proposed to reconstruct the T1ρ ‐weighted images from undersampled k‐space data and hence accelerate the acquisition of T1ρ imaging.

GcsDecolor: Gradient Correlation Similarity for Efficient Contrast Preserving Decolorization

This paper presents a novel gradient correlation similarity (Gcs) measure-based decolorization model for faithfully preserving the appearance of the original color image. Contrary to the conventional data-fidelity term consisting of gradient error-norm-based measures, the newly defined Gcs measure calculates the summation of the gradient correlation between each channel of the color image and the transformed grayscale image. Two efficient algorithms are developed to solve the proposed model. On one hand, due to the highly nonlinear nature of Gcs measure, a solver consisting of the augmented Lagrangian and alternating direction method is adopted to deal with its approximated linear parametric model. The presented algorithm exhibits excellent iterative convergence and attains superior performance. On the other hand, a discrete searching solver is proposed by determining the solution with the minimum function value from the linear parametric model-induced candidate images. The non-iterative solver has advantages in simplicity and speed with only several simple arithmetic operations, leading to real-time computational speed. In addition, it is very robust with respect to the parameter and candidates. Extensive experiments under a variety of test images and a comprehensive evaluation against existing state-of-the-art methods consistently demonstrate the potential of the proposed model and algorithms.

SGTD: Structure Gradient and Texture Decorrelating Regularization for Image Decomposition

This paper presents a novel structure gradient and texture decor relating regularization (SGTD) for image decomposition. The motivation of the idea is under the assumption that the structure gradient and texture components should be properly decor related for a successful decomposition. The proposed model consists of the data fidelity term, total variation regularization and the SGTD regularization. An augmented Lagrangian method is proposed to address this optimization issue, by first transforming the unconstrained problem to an equivalent constrained problem and then applying an alternating direction method to iteratively solve the sub problems. Experimental results demonstrate that the proposed method presents better or comparable performance as state-of-the-art methods do.

Semiparametric Decolorization With Laplacian-Based Perceptual Quality Metric

While the RGB2GRAY conversion with fixed parameters is a classical and widely used tool for image decolorization, recent studies showed that adapting weighting parameters in a two-order multivariance polynomial model has great potential to improve the conversion ability. In this paper, by viewing the two-order model as the sum of three subspaces, it is observed that the first subspace in the two-order model has the dominating importance and the second and the third subspace can be seen as refinement. Therefore, we present a semiparametric strategy to take advantage of both the RGB2GRAY and the two-order models. In the proposed method, the RGB2GRAY result on the first subspace is treated as an immediate grayed image, and then the parameters in the second and the third subspace are optimized. Experimental results show that the proposed approach is comparable to other state-of-the-art algorithms in both quantitative evaluation and visual quality, especially for images with abundant colors and patterns. This algorithm also exhibits good resistance to noise. In addition, instead of the color contrast preserving ratio using the first-order gradient for decolorization quality metric, the color contrast correlation preserving ratio utilizing the second-order gradient is calculated as a new perceptual quality metric.

Accelerated High-Dimensional MR Imaging With Sparse Sampling Using Low-Rank Tensors

High-dimensional MR imaging often requires long data acquisition time, thereby limiting its practical applications. This paper presents a low-rank tensor based method for accelerated high-dimensional MR imaging using sparse sampling. This method represents high-dimensional images as low-rank tensors (or partially separable functions) and uses this mathematical structure for sparse sampling of the data space and for image reconstruction from highly undersampled data. More specifically, the proposed method acquires two datasets with complementary sampling patterns, one for subspace estimation and the other for image reconstruction; image reconstruction from highly undersampled data is accomplished by fitting the measured data with a sparsity constraint on the core tensor and a group sparsity constraint on the spatial coefficients jointly using the alternating direction method of multipliers. The usefulness of the proposed method is demonstrated in MRI applications; it may also have applications beyond MRI.

Incorporating reference in parallel imaging and compressed sensing

To develop a new compressed sensing parallel imaging technique called READ‐PICS that can effectively incorporate prior information from a reference scan for MR image reconstruction from highly undersampled multichannel measurements.

Fenchel Duality Based Dictionary Learning for Restoration of Noisy Images

Dictionary learning based sparse modeling has been increasingly recognized as providing high performance in the restoration of noisy images. Although a number of dictionary learning algorithms have been developed, most of them attack this learning problem in its primal form, with little effort being devoted to exploring the advantage of solving this problem in a dual space. In this paper, a novel Fenchel duality based dictionary learning (FD-DL) algorithm has been proposed for the restoration of noise-corrupted images. With the restricted attention to the additive white Gaussian noise, the sparse image representation is formulated as an ℓ2-ℓ1 minimization problem, whose dual formulation is constructed using a generalization of Fenchels duality theorem and solved under the augmented Lagrangian framework. The proposed algorithm has been compared with four state-of-the-art algorithms, including the local pixel grouping-principal component analysis, method of optimal directions, K-singular value decomposition, and beta process factor analysis, on grayscale natural images. Our results demonstrate that the FD-DL algorithm can effectively improve the image quality and its noisy image restoration ability is comparable or even superior to the abilities of the other four widely-used algorithms.