基于Hessenberg测量矩阵的超声图像重建

Ultrasound imaging reconstruction based on Hessenberg matrix

针对超声图像连续性差、自身具有稀疏性的特点,提出了一种适用于超声图像的压缩感知重建方法。该方法以小波变换为稀疏基,Hessenberg矩阵为测量矩阵,引入正交匹配追踪(OMP)算法实现了超声图像的重建。超声C-扫描图像重建结果表明在观测数据采样率降低、数据缺失等条件下均能清晰的成像,验证了该方法的有效性。此外,本文给出Hessenberg测量矩阵的有限等距性(RIP)性质证明;并与基于Toeplitz测量矩阵的图像重建方法进行了比较,实验结果表明利用本文方法的重建图像在平均结构相似度(SSIM)、峰值信噪比(PSNR)和三维差值图等指标上均较优。该压缩感知重建方法在采样率为50%,原始数据较差的前提下,成功恢复出相似度在80%以上的超声图像。

This paper proposes a compressed sensing method for the reconstruction of the properties of gray level discontinuity and sparsity inherent in ultrasound images. The wavelet transform is based on a sparse transform,and a Hessenberg matrix is regarded as the measurement matrix in this method. Finally the orthogonal matching pursuit( OMP) algorithm is used to reconstruct the ultrasound image. The experimental results shows that good ultrasound C-scan images can be reconstructed even under the conditions of decreasing data sampling rate or missing observation data and the proposed method is effective. In addition,we present a simple proof of the restricted isometry property( RIP) of a Hessenberg matrix. Comparison of ultrasound reconstructed image reconstruction using Toeplitz matrix and Hessenberg matrix testify that the reconstructed ultrasound images using the proposed method have good structural similarity( SSIM),high peak signal to noise ratio( PSNR) and three dimensional error imaging,three commonly used indicators for evaluating image quality. Our method successfully recovers the ultrasonic image similarity in more than 80% of case for a sampling ratio of 50%.