Fast Minimum Variance Beamforming Based on Legendre Polynomials.

Area of Science:

• Ultrasound imaging
• Medical physics
• Signal processing

Background:

• Minimum variance (MV) beamforming enhances ultrasound image resolution but is computationally intensive.
• Existing methods to reduce MV complexity involve domain transformation and dimensionality reduction.
• Principal component analysis and beam space methods are common approaches.

Purpose of the Study:

• To introduce a novel, computationally efficient ultrasound beamforming method.
• To reduce the computational complexity of minimum variance beamforming.
• To evaluate the performance of the proposed method against existing techniques.

Main Methods:

• Developed a new beamforming method utilizing Legendre polynomials as a basis matrix for signal transformation.
• Reduced the dimensionality of the spatial covariance matrix by approximating it with key components.
• Validated the method using Field II simulations, in vitro, and in vivo experiments.

Main Results:

• The proposed Legendre polynomial method demonstrated approximation errors comparable to or lower than existing methods.
• Achieved similar or better lateral response for point targets.
• Showed improved contrast-to-speckle noise ratio in anechoic cysts compared to other methods at reduced dimensions.

Conclusions:

• The Legendre polynomial-based beamforming method offers a computationally efficient alternative for improving ultrasound image quality.
• This approach effectively reduces computational load without compromising, and potentially enhancing, image resolution and contrast.
• The method shows significant promise for practical implementation in ultrasound systems.