基于低秩理论的超声血流壁滤波器

传统的超声血流壁滤波器采用单一的截止频率,对于心跳、呼吸等因素所产生的不同组织运动滤波效果不佳。提出一种基于低秩理论的超声血流壁滤波方法。通过分析超声血流的特点,将其公式化并建立低秩模型,模型包括一个矩阵秩的最小化和一个稀疏矩阵问题。松弛后转化为最小化核范数与1范数的线性组合,成为凸优化可解问题,从而实现低秩滤波。这种滤波的创新性在于它是自适应的,同时考虑了信号的低秩性与稀疏性两个特点,通过线性组合使得滤波效果达到最优。通过低秩滤波,超声血流仿真数据得到更加精确的血流信号。对比传统的FIR滤波,分别采用12阶、56阶和92阶的FIR滤波器,得到血流信号对比实际仿真数据的RMS误差分别约为34%、16%和12%,而低秩滤波的RMS误差则低于0.001%。低秩滤波相比传统FIR滤波,不仅提高了精度,而且滤波后的信号长度不会损失。但是低秩模型计算过于复杂,因此目前还很难应用在实时的超声系统中。

Clutter Removing Filter for Ultrasound Blood Flow Imaging Based on Low Rank Model

The conventional ultrasound blood flow wall filter uses a fixed cut-off frequency, which is not effective when the tissue motion is different due to heart beat and breath. This paper presented an ultrasound clutter removing filter based on a low rank model. The characteristics of ultrasound flow signal was studied and formulated. The low rank model was comprised of a rank minimization and matrix sparsity problem. The convex optimization can be applied to solve it after relaxation. The novelty is that it is an adaptive filter due to the minimization of the combination of the nuclear norm and L₁ norm. Ultrasound blood flow data were simulated. The filtered signals were obtained by three different orders FIR filters and the low rank filter. The RMS errors for FIR filtering were around 34%, 16% and 12% respectively, and lower than 0.001% when using the low rank filter, which not only improved the accuracy a lot but also maintained the same length of the filtered signal as the original one's, where the length of the FIR filtered signal was decreased compared to the original signal. However, the low rank model is much more complicated than the conventional method, and it is still difficult to be applied in a real-time ultrasound imaging system.