Structural similarity regularized and sparse coding based super-resolution for medical images

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Abstract

Recently the single image super-resolution reconstruction (SISR) via sparse coding has attracted increasing interests. Considering that there are obviously repetitive image structures in medical images, in this study we propose a regularized SISR method via sparse coding and structural similarity. The pixel based recovery is incorporated as a regularization term to exploit the non-local structural similarities of medical images, which is very helpful in further improving the quality of recovered medical images. An alternative variables optimization algorithm is proposed and some medical images including CT, MRI and ultrasound images are used to investigate the performance of our proposed method. The results show the superiority of our method to its counterparts.

Highlights

► A method of structural similarity and sparse coding based super-resolution of medical images is proposed.

Introduction

High-resolution (HR) images are desired in medical imaging. In order to increase the resolution of medical images, we can either increase the chip size of sensors or reduce the pixel size by sensor manufacturing techniques, which are both severely constrained by the physical limitation of medical imaging systems [1]. Single image super-resolution reconstruction (SISR) can be achieved through algorithmic techniques to obtain a HR image X from an observed degraded low-resolution (LR) image Y:Y=HBX+v, where H,B,v represent the downsampling operator, blurring operator and the additive noise, respectively [2]. Depending on the communities involved, it goes by different names including resolution enhancement, HR image reconstruction and super-resolution (SR) reconstruction, which has proved to be helpful in comprehending the medical images [3], [4], [5], [6]. Regularization-based method [7], [8] and interpolation-based method [9], [10], [11] are two popular SISR schemes. Regularization methods pose some assumptions on the ill-posed image recovery problem to obtain a determined solution. However, the performance of regularization methods degrades rapidly with the increase of the magnification factor, and interpolation methods are very limited in modeling the visual complexity of the real images.

In recent years, examples-based method has attracted increasing interests [12], [13], [14], [15], [16]. Its principle is that HR image can be predicted by learning the co-occurrence relationship between a set of LR example patches and their corresponding HR version. One of representative works of examples-based SISR method is Chang's method [12], where a LR image is assumed to have similar local geometry to its corresponding HR image. Sparse coding based scheme is consequently developed, which regularizes the recovery of HR image by casting on sparse prior on the local patches. One can generate dictionaries by randomly sampling raw patches from training images of similar statistical nature, which is shown to lead to state-of-the-art result [13], [14], [15], [16]. Fig. 1 illustrates the scheme of sparse coding based SISR method.

It is well known that the preservation of details such as edges and contours is very important in computer-aided diagnosis of medical images. If the image priors such as the sparsity, smoothness, self-similarity and multiscale similarity can be incorporated into SISR, the recovery quality of medical images can be remarkably improved. Moreover, the medical images have more homogeneous regions than natural images, such as the background, bones, organs and joints in the computed tomography (CT scan) image, magnetic resonance (MR) images and ultrasound images. However, the available sparse coding based SISR methods do not make avail of other image priors except for sparse prior of patches. In this paper, we introduce structural similarity regularizer into the recovery algorithm to improve the quality of recovered images, because the non-local structural self-similarity of image has successfully improved the performance of many image processing methods [17], [18]. Using a weighted recovery constraint in a non-local region, one can enhance the detail information in the similar patches. By formulating the SISR as a multiple variables optimization problem, we can alternately optimize the variables to obtain the HR image. Some experiments are taken on comparing the performance of our proposed method with its counterparts on some CT images, MRI images and ultrasound images, and the superiorities of our proposed method to its counterparts can be observed in both the visual result and some numerical guidelines.

The rest of this paper is organized as follows. In Section 2, we depicted the structural similarity and sparse coding based SISR approach for medical images. In Section 3, some simulation experiments are taken to illustrate the efficiency and superiority of our proposed method to its counterparts. Finally some conclusions are drawn in Section 4.

Section snippets

Sparse coding based SISR

According to [15], [16], the LR image patches can be regarded as the degraded version of HR images, and two prototype dictionaries Dl (LR dictionary) and Dh (HR dictionary) are constructed, where Dh is formed by some HR prototype patches sampled from training HR images and Dl is formed by the corresponding prototype LR patches. Assuming the number of columns of the dictionaries is K and xin is the ith n×n local patch vector extracted from a HR image X at the spatial location i: xi=RiX. Ri

Experimental results

In this section, some experiments are taken to investigate the performance of our proposed method. The performance of the proposed algorithm was evaluated in experiments on some real CT images, MRI images and ultrasound images. The test LR images includes CT images, MRI images and ultrasound images, and we aim to recover their HR images (with amplifier factor be 3) from them and some example HR medical images. We compare our proposed method with Freeman's method [12], Bicubic interpolation

Conclusions

This work has investigated the sparse coding and structural similarity regularizer based single image super resolution reconstruction scheme for medical images. In this paper, under the framework of sparse coding, we incorporate a regularization term to exploit the non-local structural similarities of medical images, and reduce the image super-resolution problem to a multiple variables optimization task. The variables are alternatively tuned by our proposed optimization algorithm. Some

Acknowledgment

The authors would like to thank the anonymous reviewers for their constructive comments, which resulting much improvement of the quality of this paper. This work was supported by the National Science Foundation of China under grant nos. 61072108, 60971112, the China program NCET-10-0668 and the Foreign Scholars in University Research and Teaching Programs (the 111 Project) (Grant No. B07048).

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