We study the design of a coding mask for pulse-echo ultrasound imaging. We are interested in the scenario of a single receiving transducer with an aberrating layer, or ‘mask,’ in front of the transducer's receive surface, with a separate co-located transmit transducer. The mask encodes spatial measurements into a single output signal, containing more information about a reflector's position than a transducer without a mask. The amount of information in such measurements is dependent on the mask geometry, which we propose to optimize using an image reconstruction mean square error (MSE) criterion. We approximate the physics involved to define a linear measurement model, which we use to find an expression for the image error covariance matrix. By discretizing the mask surface and defining a discrete number of mask thickness levels per point on its surface, we show how finding the best mask can be posed as a variation of a sensor selection problem. We propose a convex relaxation in combination with randomized rounding, as well as a greedy optimization algorithm to solve this problem. We show empirically that both algorithms come close to the global optimum. Our simulations further show that the optimized masks have better a MSE than nearly all randomly shaped masks. We observe that an optimized mask amplifies echoes coming from within the region of interest (ROI), and strongly reduces the correlation between echoes of pixels within the ROI.

中文翻译：

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单传感器超声成像的编码掩模设计

我们研究了脉冲回波超声成像编码掩模的设计。我们感兴趣的是单个接收换能器的情况，在换能器的接收表面前面有一个像差层或“掩模”，有一个单独的同位发射换能器。面罩将空间测量编码为单个输出信号，与不带面罩的换能器相比，它包含更多关于反射器位置的信息。此类测量中的信息量取决于掩模几何形状，我们建议使用图像重建均方误差 (MSE) 标准对其进行优化。我们近似定义一个线性测量模型所涉及的物理，我们用它来找到图像误差协方差矩阵的表达式。通过离散掩膜表面并定义其表面上每个点的离散数量的掩膜厚度级别，我们展示了如何将寻找最佳掩膜视为传感器选择问题的变体。我们提出了凸松弛结合随机舍入，以及贪婪优化算法来解决这个问题。我们凭经验表明两种算法都接近全局最优。我们的模拟进一步表明，优化的掩码比几乎所有随机形状的掩码具有更好的 MSE。我们观察到优化的掩码放大了来自感兴趣区域 (ROI) 内的回声，并大大降低了 ROI 内像素回声之间的相关性。我们提出了凸松弛结合随机舍入，以及贪婪优化算法来解决这个问题。我们凭经验表明这两种算法都接近全局最优。我们的模拟进一步表明，优化的掩码比几乎所有随机形状的掩码具有更好的 MSE。我们观察到优化的掩码放大了来自感兴趣区域 (ROI) 内的回声，并大大降低了 ROI 内像素回声之间的相关性。我们提出了凸松弛结合随机舍入，以及贪婪优化算法来解决这个问题。我们凭经验表明这两种算法都接近全局最优。我们的模拟进一步表明，优化的掩码比几乎所有随机形状的掩码具有更好的 MSE。我们观察到优化的掩码放大了来自感兴趣区域 (ROI) 内的回声，并大大降低了 ROI 内像素回声之间的相关性。