Na Qi

Two dimensional synthesis sparse model

Sparse representation has been proved to be very efficient in machine learning and image processing. Traditional image sparse representation formulates an image into a one dimensional (1D) vector which is then represented by a sparse linear combination of the basis atoms from a dictionary. This 1D representation ignores the local spatial correlation inside one image. In this paper, we propose a two dimensional (2D) sparse model to much efficiently exploit the horizontal and vertical features which are represented by two dictionaries simultaneously. The corresponding sparse coding and dictionary learning algorithm are also presented in this paper. The 2D synthesis model is further evaluated in image denoising. Experimental results demonstrate our 2D synthesis sparse model outperforms the state-of-the-art 1D model in terms of both objective and subjective qualities.

Two dimensional analysis sparse model

An analysis sparse model represents an image signal by multiplying it using an analysis dictionary, leading to a sparse outcome. It transforms an image (two dimensional signal) into a one-dimensional (1D) vector. However, this 1D model ignores the two dimensional property and breaks the local spatial correlation inside images. In this paper, we propose a two dimensional (2D) analysis sparse model. Our 2D model uses two analysis dictionaries to efficiently exploit the horizontal and vertical features simultaneously. The corresponding sparse coding and dictionary learning algorithm are also presented in this paper. The 2D sparse model is further evaluated for image denoising. Experimental results demonstrate our 2D analysis sparse model outperforms a state-of-the-art 1D analysis model in terms of both denoising ability and memory usage.

Realistic mesh compression based on geometry image

In order to show the realistic 3D mesh in geometry image-based 3D mesh compression, in addition to coding geometry image, normal-map image is usually required to code. But normal-map image are difficult to compress because it captures more details of the original mesh, and it has less spatial correlation between pixels than geometry image. This paper proposes a novel coding framework to solve this problem, we effectively predict the normal-map image based on the correlation between geometry image and normal-map image, and we also utilize the strong correlation among three components of normal-map image to improve the predicting accuracy. In this framework we only need to code geometry image and residual image which generated from normal-map image and its prediction. Experimental results show that comparing with the method which coding geometry image and normal-map image using JPEG2000 directly, our coding framework not only improves the coding efficiency of geometry images and normal-map images, but also enhances the realistic effect of 3D mesh significantly.

TenSR: Multi-dimensional Tensor Sparse Representation

The conventional sparse model relies on data representation in the form of vectors. It represents the vector-valued or vectorized one dimensional (1D) version of an signal as a highly sparse linear combination of basis atoms from a large dictionary. The 1D modeling, though simple, ignores the inherent structure and breaks the local correlation inside multidimensional (MD) signals. It also dramatically increases the demand of memory as well as computational resources especially when dealing with high dimensional signals. In this paper, we propose a new sparse model TenSR based on tensor for MD data representation along with the corresponding MD sparse coding and MD dictionary learning algorithms. The proposed TenSR model is able to well approximate the structure in each mode inherent in MD signals with a series of adaptive separable structure dictionaries via dictionary learning. The proposed MD sparse coding algorithm by proximal method further reduces the computational cost significantly. Experimental results with real world MD signals, i.e. 3D Multi-spectral images, show the proposed TenSR greatly reduces both the computational and memory costs with competitive performance in comparison with the state-of-the-art sparse representation methods. We believe our proposed TenSR model is a promising way to empower the sparse representation especially for large scale high order signals.

Multi-Dimensional Sparse Models

Traditional synthesis/analysis sparse representation models signals in a one dimensional (1D) way, in which a multidimensional (MD) signal is converted into a 1D vector. 1D modeling cannot sufficiently handle MD signals of high dimensionality in limited computational resources and memory usage, as breaking the data structure and inherently ignores the diversity of MD signals (tensors). We utilize the multilinearity of tensors to establish the redundant basis of the space of multi linear maps with the sparsity constraint, and further propose MD synthesis/analysis sparse models to effectively and efficiently represent MD signals in their original form. The dimensional features of MD signals are captured by a series of dictionaries simultaneously and collaboratively. The corresponding dictionary learning algorithms and unified MD signal restoration formulations are proposed. The effectiveness of the proposed models and dictionary learning algorithms is demonstrated through experiments on MD signals denoising, image super-resolution and texture classification. Experiments show that the proposed MD models outperform state-of-the-art 1D models in terms of signal representation quality, computational overhead, and memory storage. Moreover, our proposed MD sparse models generalize the 1D sparse models and are flexible and adaptive to both homogeneous and inhomogeneous properties of MD signals.

Single image super-resolution via 2D nonlocal sparse representation

Image super-resolution based on sparse model with patch clustering and nonlocal similarity provides promising performance. However, the traditional one dimensional (1D) sparse model enforces a 1D dictionary for every cluster of patches to capture complex structures and different features in images. The total dictionary will take expensive memory, which can be alleviated at cost of representation power. Recently, two dimensional (2D) sparse model has been proved to efficiently represent images and save memory usage. In this paper, we propose to integrate 2D sparse model with patch clustering and nonlocal similarity into a variational framework as 2D nonlocal sparse representation (2DNSR) for image SR to save memory cost and ensure SR performances. We also present a 2DNSR algorithm for image SR where each group of similar patches decompose on the respective 2D dictionaries. Experimental results on image SR demonstrate our proposed 2D nonlocal representation outperforms 2D sparse model and achieves competitive performance to state-of-the-art 1D nonlocal sparse models whereas with much less memory costs.

Two dimensional K-SVD for the analysis sparse dictionary

Analysis sparse model has been successfully used for a variety of tasks such as image denoising, deblurring, and most recently compressed sensing, so it arouses much attention. K-SVD is a mature dictionary learning approach for the analysis sparse model. However, it represents images as one dimension signals, which results in mistakes of spatial correlations. In this paper, we propose a novel analysis sparse model, where analysis dictionary derived from two analysis operators which act on an image, leading to a sparse outcome. And a two dimensional K-SVD (2D-KSVD) is proposed to train the analysis sparse dictionaries. Experiments on image denoising validate that the proposed analysis dictionary can express more image spatial and frequency characteristics and by using the dictionary, the two dimension analysis sparse model outperforms the traditional analysis model in terms of PSNR.

2D nonlocal sparse representation for image denoising

Two dimensional (2D) sparse representation provides promising performance in image denoising by cooperatively exploiting horizontal and vertical features inherent in images by two dictionaries. In this paper, we first propose integrating the 2D sparse model with clustering and nonlocal regularization into a unified variational framework, defined as 2D nonlocal sparse representation (2DNSR), for optimization. Within this framework, we then present a dictionary learning method for image denoising which jointly decomposes groups of similar noisy patches on subsets of 2D dictionaries. We finally present a 2DNSR-based algorithm for image denoising. Experimental results on image denoising show our proposed 2D nonlocal sparse representation outperforms the 2D sparse model and achieves competitive performance to state-of-the-art nonlocal sparse models whereas with much less memory costs.

Prediction-based realistic 3D model compression

The benefit of using the geometry image to represent an arbitrary 3D mesh is that the 3D mesh can be re-sampled as a completely regular structure and coded efficiently by common image compression methods. For geometry image-based 3D mesh compression, we need to code the normal-map images while coding geometry images to improve the subjective quality and realistic effects of the reconstructed model. In traditional methods, a geometry image and a normal-map image are coded independently. However a strong correlation exists between these two kinds of images, because both of them are generated from the same 3D mesh and share the same parameterization. In this paper we propose a predictive coding framework, in which the normal-map image is predicted based on the geometric correlation between them. Additionally we utilize the strong geometric correlation among three components of normal-map image to improve the predicting accuracy. The experimental results show the proposed coding framework improves the coding efficiency of normal-map image, meanwhile the realistic effect of a 3D mesh is significantly enhanced.