波束形成是医学超声系统中至关重要的一个步骤，其算法直接影响超声成像的质量。传统的延时叠加波束形成方法简单易行，广泛应用于现有医学超声系统中，但是其成像结果面临着横向分辨率较低和旁瓣较高的问题。为解决此问题，有关学者提出了许多优秀算法，使得超声成像的分辨率和对比度得到了极大地提升，但是其性能的提高是以计算复杂度地剧增为代价的，制约着其工程应用。因此，研究具有高效计算能力、性能良好的波束形成算法，已成为当今医学超声波束形成算法研究的热点与难点，它是医学超声成像质量提高的重要保障，有着巨大的研究意义和市场价值。 本文针对此问题，基于不同的超声成像系统，以波束形成算法为研究对象，降低计算复杂度为研究主线，从时域、波束域、平面波和变换域四个角度展开了深入和系统地研究，提出了相应的、各具特色的具有较低计算复杂度的波束形成算法。主要的研究成果如下： 1.以时域波束形成算法为基础，提出了一种子阵平均延时组合乘叠加波束形成算法。本算法旨在降低延时组合乘叠加波束形成算法的计算复杂度，提高成像性能。首先对延时组合乘叠加算法进行重新演绎，构建了等价的、以矩阵为最小计算单元的表达式，其中该矩阵由回波信号的协方差矩阵构成。然后将子阵平均技术引入该算法用以降低接收回波信号之间的相关性。最后通过添加回波信号的自相关成分，用来增加延时组合乘叠加算法中的能量强度。该矩阵形式的波束形成算法，不仅可以降低计算复杂度，而且减少了所需的存储空间和硬件开销。仿真和实验结果验证了算法的有效性。结果表明，与延时组合乘叠加算法相比，该算法不仅有效地提高了成像性能，而且计算复杂度降低了66.6％。 2.以波束域波束形成算法为基础，提出了一种波束域延时组合乘叠加波束形成算法。为了降低波束域最小方差波束形成算法的计算复杂度，首次将延时组合乘叠加波束形成算法应用于波束域，并从理论和实验两方面研究其可行性。首先基于离散余弦变换构建了抽取的正交矩阵，用于降低波束域信号的维数。然后推导了一种延时组合乘叠加波束形成的并行算法，并将其应用于波束域。借助于简单的开平方根、符号运算和加法运算即可得到最终的波束形成结果。与波束域最小方差方法相比，避免了通过计算协方差矩阵及逆矩阵得到自适应权重的过程，计算复杂度由PM+P³+3P²+O(P)降低到PM+P²+O(P)。最后仿真和实验结果验证了算法的有效性。结果表明，所提算法具有较好的分辨率、对比度、较低的计算复杂度和较强的鲁棒性。 3.以平面波波束形成算法为基础，提出了一种延时组合乘叠加与符号相干因子相结合的波束形成算法。本算法旨在结合符号相干因子和延时组合乘叠加波束形成的优点，解决平面波复合成像质量不高和计算复杂度偏高的问题。首先构建2维回波信号数据集。然后在此基础上分别计算每次发射的平面波所对应的符号相干因子和延时组合乘叠加波束形成结果，并且将信号自相关成分引入到延时组合乘叠加波束形成中。最后根据两者的计算结果，构建了基于2维回波信号数据集的平面波波束形成模型。由于符号相干因子简单、易硬件实现，且该算法以矩阵为最小的计算单元，可以有效地降低计算复杂度，提高成像速度(帧率)。仿真结果验证了方法的有效性。结果表明，与传统的平面波复合成像算法相比，该算法的横向分辨率获得了极大的提高。同时，在不降低帧频的情况下，对比度和对比噪声率分别提高了96.97％和79.98％。 4.以变换域波束形成算法为基础，提出了一种余弦变换域最小方差波束形成算法。本算法旨在解决变换域波束形成计算复杂度高，硬件难以实现的问题。首先构建抽取的离散余弦变换矩阵，该矩阵不仅能将时域信号投影到低维的余弦变换域上，同时可以保留时域信号的所有性质。其次借助所构建矩阵的正交性，将时域的最小方差波束形成算法移植到该变换域上。最后对最小方差波束形成算法进行重新演化，建立了其基于离散余弦变换的并行模型。仿真和实验结果验证了算法的有效性。结果表明，与时域的最小方差波束形成相比，该算法在横向分辨率、对比度和鲁棒性提高的同时，计算复杂度由O(L³)降低到O(PL²)。 总之，本文为实现降低计算复杂度，提高超声成像质量的目标，针对不同系统的波束形成算法，主要进行了如下的尝试：一是将矩阵作为最小的数据处理单元；二是借助离散余弦变换对回波数据进行压缩；三是构建抽取的正交变换矩阵用以降维。在此基础上所提出的波束形成算法均通过了仿真和实验验证。为现有的医学超声成像系统质量的提高提供技术和理论支持，有一定的学术价值和实用价值。 关键词：超声成像；波束形成；波束域；平面波；符号相干因子；计算复杂度；离散余弦变换

 Beamforming algorithm is an important step in medical ultrasound system, which affects the quality of ultrasound image. The traditional delay and sum (DAS) beamforming is simple and easy to implement, which is widely used in the existing medical ultrasound system. However, the imaging results are suffered from low later resolution and high level side lobes. To address this problem, many new excellent algorithms have been proposed, which greatly improve the resolution and contrast of ultrasound imaging. Unfortunately, the improvement of its performance is at the cost of increasing computational complexity, which restricts its engineering application. Therefore, seeking for an innovation algorithm with better performance and lower complex to real-time imaging has become one hot issue in study of ultrasound beamforming. It is an important guarantee for improving the quality of medical ultrasound imaging equipment in our country and has great research significance and market value. In this thesis, to focus on this problem, based on different ultrasound imaging systems, taking the beamforming as the research object and reducing the computational complexity as the research main line, the in-depth and systematic research is carried out from four aspects. These four aspects include time domain, beam-space, plane wave and transform domain. Furthermore, corresponding characteristic beamforming algorithms with lower computational complexity are proposed. The main research works of this paper are as follows: 1.Based on the time domain beamforming algorithm, sub-array average delay multiply and sum (SA-DMAS) beamforming algorithm is proposed. The algorithm is designed to reduce the computational complexity and improve the imaging performance of delay multiply and sum beamforming. Firstly, by reanalyze the delay multiply and sum beamforming, an equivalent expression with matrix as the minimum element is constructed. The matrix is composed of the covariance matrix of the echo signal. 2-D echo data set firstly, which improves the imaging speed greatly. Then, the results of sign coherent factor and DMAS beamforming for each transmitting are calculated, respectively. Furthermore, the auto-correlation components are introduced into the DMAS beamforming. Finally, based on the calculation results of the two, a plane wave beamforming model based on the 2D echo signal data-set is constructed. Due to the sign coherent factor is simple and easy realized by hardware, and the smallest computing unit is in matrix form, which can effectively reduce the computational complexity and improve the imaging speed (frame rate). The simulation is used to evaluate the performance of proposed method. Results show that, compared with the traditional plane wave imaging, the lateral resolution of SCF-DMAS beamforming improves greatly for the point targets, and for the cyst phantom, the contrast ratio (CR) and contrast-to-noise ratio (CNR) increased by 96.97% and by 79.98% respectively without reducing the frame rate. 4.Based on the transform domain beamforming algorithm, a discrete cosine transform minimum variance beamforming (DCTMV) is proposed. This algorithm aims at reducing computational complexity without increasing hardware cost in transform domain beamforming. Firstly, the decimation cosine transform matrix is constructed. By using this matrix, not only the time domain signal is projected onto low-dimensional cosine transform domain, but also the properties of the time domain signal are preserved. Then, by means of the orthogonality of the decimation matrix, the minimum variance beamforming can be transplanted to the transform domain directly. Finally, the minimum variance beamforming is re-deduced, and the corresponding parallel processing model in the discrete cosine transform domain is established. Simulation and experimental results verify the effectiveness of the method. The results show that, compared with the minimum variance beamforming in time domain, the computational complexity is reduced from 0(L³) to 0(PL²), at the same time, the resolution and contrast is improved. In addition, the proposed method is robust to noise. In summary, in this paper, in order to reduce the computational complexity and improve the quality of ultrasound imaging, the following attempts are made for the beamforming algorithms of different systems. One is to use the matrix as the minimum data processing unit. The second is to use the discrete cosine transform to compress the echo data. The third is to construct the decimation orthogonal transformation matrix to reduce the dimension. The corresponding beamforming method are established and verified by simulation and experiment. It has academic and practical value and provides technical and theoretical support for improvement of the quality of existing medical ultrasound imaging systems. Key words: Ultrasound imaging; Beamforming; Beam domain; Plane wave; Sign coherent factor; Computational complexity; Discrete cosine transform