A low-complexity adaptive beamformer for ultrasound imaging using structured covariance matrix

Abstract

In recent years, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in simultaneous improvement in imaging resolution and contrast. These improvements have been achieved at the expense of higher computational complexity, with respect to the conventional non-adaptive delay-and-sum (DAS) beamformer, in which computational complexity is proportional to the number of elements, O(M). The computational overhead results from the covariance matrix inversion needed for computation of the adaptive weights, the complexity of which is cubic with the subarray size, O(L(3)). This is a computationally intensive procedure, which makes the implementation of adaptive beamformers less attractive in spite of their advantages. Considering that, in medical ultrasound applications, most of the energy is scattered from angles close to the steering angle, assuming spatial stationarity is a good approximation, allowing us to assume the Toeplitz structure for the estimated covariance matrix. Based on this idea, in this paper, we have applied the Toeplitz structure to the spatially smoothed covariance matrix by averaging the entries along all subdiagonals. Because the inverse of the resulting Toeplitz covariance matrix can be computed in O(L(2)) operations, this technique results in a greatly reduced computational complexity. By using simulated and experimental RF data-point targets as well as cyst phantoms-we show that the proposed low-complexity adaptive beamformer significantly outperforms the DAS and its performance is comparable to that of the minimum variance beamformer, with reduced computational complexity.

A Sibelobe Suppressing Beamformer for Coherent Plane Wave Compounding

“…Since the matrix is a square matrix, the SVD equals the eigen-decomposition. The eigen-decomposition of the covariance matrix requires 21n 3 floating operations by using the Golub-Reinsch algorithm [29]. In other words, the computational amount is proportional to the cube of the angle number.…”

Special Issue on Ultrafast Ultrasound Imaging and Its Applications

“…Significant improvements in image quality can be realized by minimum variance beamforming. On the other hand, the computational complexity of the minimum variance beamformer is very high, and developments of efficient implementations of the minimum variance beamformer are still ongoing [12,13]. In addition, various studies on improvement in the performance of the minimum variance beamformer have been conducted [14,15].…”

Low-Complexity Adaptive Sonar Imaging

“…This can be dealt with by approximating the full covariance matrix with a small one using space reduction techniques such as beamspace processing [6], or the closely related principal component analysis (PCA) method [7]. Another alternative is to assume spatial stationarity to form more easily invertible Toepliz matrices [8]. However, the mentioned methods are still relatively slow compared to DAS.…”