## 1 Introduction  
Because of its safety and non-invasiveness, ultrasound imaging is commonly used in medical applications. The plane-wave method is a conventional way to achieve ultrafast ultrasound imaging, and has been applied in various new ultrasound technologies with high frame rate requirements [1; 2; 3]. In the field of plane-wave imaging, researches have been focused on improving the imaging speed and imaging quality. A high frame rate imaging method based on the Fourier spectrum of the object function using the limited diffraction beams was developed by [PERSON] et al. to accelerate image formation [4; 5]. Compressed sensing has been successfully applied for fast image acquisition in pulse-echo ultrasound [6; 7]. Furthermore, the convolutional neural network (CNN) was successfully implemented to learn a compounding operation from data, and thus reconstruct high-quality images using a small number of transmissions [8]. [PERSON] et al. [9] coherently compounded plane-waveswith different steering angles to obtain equivalent quality but higher frame rate images compared to B-mode multi-focus imaging. This technique was named coherent plane-wave compounding (CPWC). However, because CPWC uses the delay-and-sum (DAS) beamformer to construct images, it suffers from poor resolution and high sidelobes. Therefore, many new developments have been taking place in the field of adaptive beamforming techniques with the aim of improving CPWC image quality. Adaptive beamforming methods based on the coherence of echo signals to select weighting factors have a better capability in terms of resolution improvement and interference rejection as compared to DAS [10; 11]. The coherence factor (CF)--defined as the ratio between the energy of the coherent sum and the incoherent sum of the signal--can suppress sidelobes and improve image contrast [12; 13]. The generalized coherence factor (GCF) is a robust CF, which is defined as the ratio of the spectral energy in the low-frequency region to the total energy [14]. Ultrasonic speckle is an interference effect caused by the scattering of the ultrasonic beam from microscopic tissue inhomogeneities [15], and it provides useful information about the underlying microstructure. Speckle has been demonstrated as being valuable in medical imaging and speckle tracking techniques have been applied to cardiac imaging and blood speckle imaging [16; 17]. It has been found that in vivo tissue and diffuse scatters have similar coherence [18]. Due to the randomness of diffuse scatters, speckle-generating targets contain a degree of incoherence. GCF tends to preserve part of the incoherence in echo signals from speckle by including a part of high-frequency components. Thus, it preserves the speckle pattern better, but has higher sidelobe levels compared to CF. Furthermore, CF and GCF have been demonstrated to have good imaging performances in CPWC imaging [19; 20]. [PERSON] et al. [21] proposed a modified CF for CPWC, named dynamic coherence factor (DCF). DCF introduces a normalized standard deviation to evaluate the angular difference of different steered plane-waves, and then uses several plane-wave imaging results with a small angular difference to calculate CF. Because DCF could evaluate the coherence of steered plane-wave signals more accurately than CF, images obtained by DCF weighted CPWC showed a higher contrast. A united sign coherence factor (uSCF) [22] was proposed for contrast and resolution enhancements in CPWC imaging. Short-lag spatial coherence (SLSC), which uses the spatial coherence of the backscattered echo signals to calculate weighting factors, was studied to weigh CPWC images [18; 23]. It has been shown that SLSC beamforming can reduce clutter and sidelobes. SLSC images provide a superior speckle signal-to-noise ratio (sSNR) and CNR compared to DAS images, but with reduced contrast. SLSC was also studied for use as a weighting factor. The study of [PERSON] et al.