A fast algorithm for high-resolution acoustic image measurement using polar coordinate deconvolution
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摘要:
二维反卷积声图测量中点扩散函数(PSF)的二维移变性导致算法计算量较大, 为此提出了一种极坐标系下方位、距离分离降维处理的快速反卷积声图测量方法。该方法将二维移变反卷积运算转换为两次一维反卷积运算, 同时利用方位维反卷积具有近似一维空域移不变特点, 采用移不变模型进行计算, 仅对距离维进行一维移变反卷积运算, 从而减少算法的PSF存储空间和计算量。仿真和实验数据处理结果表明, 所提方法显著降低了计算量, 且与原二维移变模型反卷积声图测量方法的性能相近。
Abstract:For the huge computational complexity caused by the two-dimensional shift-variant specialty of point spread function (PSF) in two-dimensional deconvoluted acoustic image measurement, this paper proposes a fast algorithm of acoustic image measurement using polar coordinate deconvolution that separates azimuth and distance domain to make a dimension-reduced processing. The proposed method converts the two-dimensional shift-variant deconvolution into two one-dimensional deconvolutions, and utilizes the approximate spatial shift-invariant characteristic of the one-dimensional deconvolution in the azimuth domain at the same time. By selecting the shift-invariant model to realize the deconvolution here, only the shift-variant deconvolution is conducted in the distance domain, thereby reducing the PSF storage space and computational complexity. The results of simulation and experimental data processing show that the proposed method significantly reduces the computational complexity with the similar performance compared to the original two-dimensional shift-variant deconvolution algorithm.
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图 2 指向不同角度的声图PSF结果 (a)
{\boldsymbol R}(\left. {r,\theta } \right|80{\text{ m}},{90{\text{°}} }) ; (b){\boldsymbol R}(\left. {r,\theta } \right|80{\text{ m}},{\text{8}}{{\text{0}}{\text{°}} }) ![]()
图 4 不同距离时声图PSF及方位维PSF束宽对比 (a)
{\boldsymbol R}(\left. {r,\theta } \right|80{\text{m}},{90{\text{°}} }) ; (b){\boldsymbol R}(\left. {r,\theta } \right|{\text{10}}0{\text{m}},{90{\text{°}} }) ; (c){\boldsymbol R}(\left. {r,\theta } \right|{\text{12}}0{\text{m}},{90{\text{°}} }) ; (d) 声源位于不同距离时方位维PSF![]()
图 5 相同方位不同距离及不同方位相同距离的目标PSF对比 (a) 距离维PSF
{\boldsymbol R}(\left. {r,\theta } \right|{\text{6}}0{\text{m}},{90{\text{°}} }) ; (b) 距离维PSF{\boldsymbol R}(\left. {r,\theta } \right|{\text{10}}0{\text{m}},{90{\text{°}} }) ; (c)r = 100{\text{ m}} 时不同方位距离维PSF切片; (d) 距离维PSF表 1 本文方法求解过程
(1) 输入 接收信号{{\boldsymbol{x}}}, 声源信号方向向量{{\boldsymbol{A}}}\left( {r,\theta } \right), 扫描区域起止点\theta ',\theta '',r',r'';
阵元数: M; 迭代次数: {\alpha _{\max }}, 终止门限: e; 常规聚焦波束形成输出: {\boldsymbol P}\left( {r,\theta } \right);
方位维PSF函数: {{\boldsymbol R}_{{r_i}}}\left( {\cos \theta - \cos \vartheta } \right);
距离维PSF矩阵: {{\boldsymbol R}_{\cos {\theta _j}}}\left( {r\left| \zeta \right.} \right)(2) 初始化 {\boldsymbol S}_{{r_i}}^{\left( 0 \right)}\left( {\cos \vartheta } \right) = {{\boldsymbol P}_{{r_i}}}\left( {\cos \vartheta } \right), {\boldsymbol S}_{\cos {\theta _j}}^{\left( 0 \right)}\left( \zeta \right) = {{\boldsymbol P}_{\cos {\theta _j}}}\left( \zeta \right) (3) 循环 方位维:
1) 由式(3)得到{\boldsymbol P}\left( {r,\theta } \right);
2) 取{\boldsymbol P}\left( {r,\theta } \right)的第i行, 记为{{\boldsymbol P}_{{r_i}}}\left( {\cos \theta } \right);
3) 代入式(10), 逐次迭代, 得到{\boldsymbol S}_{{r_i}}^{\left( {\alpha + 1} \right)}\left( {\cos \vartheta } \right);距离维:
1) 由式(3)得到{\boldsymbol P}\left( {r,\theta } \right);
2) 取{\boldsymbol P}\left( {r,\theta } \right)的第j列, 记为{{\boldsymbol P}_{\cos {\theta _j}}}\left( r \right);
3) 代入式(14), 逐次迭代, 得到{\boldsymbol S}_{\cos {\theta _j}}^{\left( {\alpha + 1} \right)}\left( \zeta \right)终止条件 如果\alpha \lt {\alpha _{\max }}, 令\alpha = \alpha + 1, 返回步骤(3);
若\big\| {{\boldsymbol S}_{{r_i}}^{\left( {\alpha + 1} \right)}\left( {\cos \vartheta } \right) - {\boldsymbol S}_{{r_i}}^{\left( \alpha \right)}\left( {\cos \vartheta } \right)} \big\| + \big\| {{\boldsymbol S}_{\cos {\theta _j}}^{\left( {\alpha + 1} \right)}\left( \zeta \right) - {\boldsymbol S}_{\cos {\theta _j}}^{\left( \alpha \right)}\left( \zeta \right)} \big\| < e, 迭代终止。(4) 输出 1) {\boldsymbol S}_{{r_i}}^{\left( {\alpha + 1} \right)}\left( {\cos \vartheta } \right)为方位维反卷积输出;
2) {\boldsymbol S}_{\cos {\theta _j}}^{\left( {\alpha + 1} \right)}\left( \zeta \right)为距离维反卷积输出;
将 1) 与 2) 的结果代入式(15)得到极坐标系下二维反卷积输出。
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