Michailovich Oleg, Adam Dan
Department of Biomedical Engineering, Technion-Israel Institute of Technology, Haifa.
IEEE Trans Med Imaging. 2003 Mar;22(3):368-81. doi: 10.1109/TMI.2003.809603.
A different approach to the problem of estimation of the ultrasound pulse spectrum, which usually arises as a part of ultrasound image restoration algorithms, is presented. It is shown that this estimation problem can be reformulated in terms of a de-noising problem. In this formulation, the log-spectrum of a radio-frequency line (RF-line) is viewed as a noisy measurement of the signal that needs to be estimated, i.e., the ultrasound pulse log-spectrum. The log-spectrum of the tissue reflectivity function (i.e., tissue response) is considered as the noise to be rejected. The contribution of the paper is twofold. First, it provides statistical description of the reflectivity function log-spectrum for the case, when the samples of the reflectivity function are independent identically distributed (i.i.d.) Gaussian random variables. Moreover, it is shown that the problem of the pulse spectrum recovery is essentially a de-noising problem. Consequently, it is suggested to solve the problem within the framework of the de-noising by wavelet shrinkage. Second, a computationally efficient algorithm is proposed for the pulse-spectrum estimation, which can be viewed as a modified version of the classical Donoho's three-step de-noising procedure. This modification is necessary, because of specific properties of the noise to be rejected. It is shown, that whenever the samples of the reflectivity function can be assumed to be i.i.d. Gaussian random variables, the samples of its log-spectrum obey the Fisher-Tippet distribution. For this type of noise, straightforward implementation of the standard de-noising can cause serious estimation errors. In order to overcome this difficulty, an outlier-resistant de-noising is performed. The unique properties of this modified de-noising algorithm allow estimating the pulse spectrum adaptively to its properties, as they are continuously influenced by the frequency-dependent attenuation process. The performance of the proposed algorithm is examined in a series of computer-simulations. It is shown that this algorithm, developed on the assumption of the "Gaussian" reflectivity function, remains applicable for broader classes of distributions. The results obtained in a series of in vivo experiments reveal superior performance of the novel approach over some of alternative estimation techniques, e.g., cepstrum-based estimation.
本文提出了一种针对超声脉冲谱估计问题的不同方法，该问题通常作为超声图像恢复算法的一部分出现。结果表明，这个估计问题可以根据去噪问题重新表述。在此表述中，射频线（RF线）的对数谱被视为需要估计的信号（即超声脉冲对数谱）的有噪声测量。组织反射率函数（即组织响应）的对数谱被视为要去除的噪声。本文的贡献有两方面。首先，它提供了反射率函数对数谱的统计描述，适用于反射率函数样本为独立同分布（i.i.d.）高斯随机变量的情况。此外，结果表明脉冲谱恢复问题本质上是一个去噪问题。因此，建议在小波收缩去噪框架内解决该问题。其次，提出了一种计算效率高的脉冲谱估计算法，它可以看作是经典的多诺霍三步去噪过程的修改版本。由于要去除的噪声的特殊性质，这种修改是必要的。结果表明，只要反射率函数的样本可以假定为i.i.d.高斯随机变量，其对数谱的样本就服从费希尔 - 蒂皮特分布。对于这种类型的噪声，直接实施标准去噪可能会导致严重的估计误差。为了克服这个困难，进行了抗异常值去噪。这种修改后的去噪算法独特的特性允许根据脉冲谱的特性进行自适应估计，因为它们不断受到频率相关衰减过程的影响。在一系列计算机模拟中检验了所提出算法的性能。结果表明，这种基于“高斯”反射率函数假设开发的算法仍然适用于更广泛的分布类别。在一系列体内实验中获得的结果表明，这种新方法比一些替代估计技术（例如基于倒谱的估计）具有更好的性能。
