Non-stationary blind deconvolution of medical ultrasound scans
Non-stationary blind deconvolution of medical ultrasound scans
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医学超声扫描的非平稳盲反卷积
DOI：
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发表时间：
2017
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通讯作者：
O. Michailovich
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作者：
O. Michailovich
在线性近似中，射频（RF）超声图像的形成可以基于标准卷积模型来描述，其中图像是通过超声扫描仪的点扩散函数（PSF）与组织反射率函数（TRF）进行卷积而获得的。由于 PSF 的频带限制性质，RF 图像只能以有限的空间分辨率获取，这通常不足以正确表示 TRF 中包含的诊断信息。缓解这个问题的一种特殊方法是通过图像反卷积，当同时估计 PSF 和 TRF 时，图像反卷积通常以“盲”模式执行。尽管盲解卷积 (BD) 已被证明是有效的，但它仍然存在许多缺点，其中最主要的缺点是它依赖于静态卷积模型，而该模型无法考虑 PSF 的空间变异性。因此，几乎所有现有的 BD 算法都应用于 RF 图像的局部片段。在这项工作中，我们引入了一种新的非平稳 BD 方法，该方法能够同时恢复 TRF 和空间可变 PSF。特别是，我们的方法基于半群理论，它允许人们根据正确定义的线性半群的作用来描述这种 PSF 的效果。该方法导致了一个易于处理的优化问题，可以使用标准数值方法来解决。体内超声数据的实验支持了所提出的解决方案的有效性。
In linear approximation, the formation of a radio-frequency (RF) ultrasound image can be described based on a standard convolution model in which the image is obtained as a result of convolution of the point spread function (PSF) of the ultrasound scanner in use with a tissue reflectivity function (TRF). Due to the band-limited nature of the PSF, the RF images can only be acquired at a finite spatial resolution, which is often insufficient for proper representation of the diagnostic information contained in the TRF. One particular way to alleviate this problem is by means of image deconvolution, which is usually performed in a “blind” mode, when both PSF and TRF are estimated at the same time. Despite its proven effectiveness, blind deconvolution (BD) still suffers from a number of drawbacks, chief among which stems from its dependence on a stationary convolution model, which is incapable of accounting for the spatial variability of the PSF. As a result, virtually all existing BD algorithms are applied to localized segments of RF images. In this work, we introduce a novel method for non-stationary BD, which is capable of recovering the TRF concurrently with the spatially variable PSF. Particularly, our approach is based on semigroup theory which allows one to describe the effect of such a PSF in terms of the action of a properly defined linear semigroup. The approach leads to a tractable optimization problem, which can be solved using standard numerical methods. The effectiveness of the proposed solution is supported by experiments with in vivo ultrasound data.