The application of k-space in pulse echo ultrasound

Abstract

K-space is a frequency domain description of imaging systems and targets that can be used to gain insight into image formation. Although originally proposed in ultrasound for the analysis of experiments involving anisotropic scattering and for the design of acoustic tomography systems, it is particularly useful for the analysis of pulse echo ultrasonic imaging systems. This paper presents analytical and conceptual techniques for estimating the k-space representation of pulse echo imaging systems with arbitrary transmit and receive array geometries and apodizations. Simple graphical methods of estimating the first and second order statistics of speckle are presented. Examples are presented that utilize k-space to gain insight regarding the performance of spatial and frequency compounding and to describe the impact of synthetic receive aperture geometry on beamforming and speckle statistics. The Van Cittert-Zernike theorem is presented in k-space, and techniques for improving echo coherence are discussed.

Ultrasound Image Denoising by Spatially Varying Frequency Compounding

“…Therefore, it is desirable that compounding would account for this spatial correlation. -Speckles in different images of the same object, acquired with different acoustic frequencies, are correlated [13]. Therefore, simple averaging is not very efficient for speckle reduction.…”

Phased subarray imaging for low-cost, wideband coherent array imaging

“…In the spatial domain, this corresponds to estimating the zero-valued beam samples between the acquired beams. In the spatial frequency domain, or k-space [6], the filters are designed to suppress the aliases that result from upsampling while simultaneously preserving the desired response. Figure 1 illustrates the role of the interpolation filter in k-space.…”

K-space model of motion artifacts in synthetic transmit ultrasound imaging

“…One can use the Fraunhofer approximation to describe it. The Fraunhofer approximation is valid in two cases: (a) the far field, and (b) the focal point in the case of a focused transducer [5,6]. It basically states that the radiated field and the apodization functions are related through the Fourier transform 1 :…”

“…The figure shows the 2-D case of a transducer which is focused at 1 The exact expressions can be taken from one of the references Ref. [1,5,6] a fixed point x f = (0, z f ). The center of the transducer coincides with the origin of the coordinate system (0,0).…”

“…As pointed out in [5] simple graphical methods are useful for the intuitive understanding of the image formation, and can be used also as an excellent teaching tool. The main contribution of this paper is that the geometrical model is given in 2-D rather than 1-D (most other papers consider only A(x), rather than p(x, z)).…”