## 1 Introduction  
Ultrasound plane-wave imaging (PWI) can significantly increase the frame rate and thus realize ultrafast imaging (\(>\)1000 frames per second) [1]. It has been widely studied because of the increasing need for high frame rates in medical ultrasound imaging over the past several decades [2, 3]. Nevertheless, the absence of transmit focusing leads to a low signal-to-noise ratio (SNR) of echo signals and thus causes a poor image quality. To address this problem, [PERSON] et al. [4] proposed coherent plane-wave compounding (CPWC) ultrasound imaging, which improves the resolution and contrast without compromising the high frame rate. It can achieve at least a similar image quality to conventional focused imaging with dynamic receive focusing [5, 6, 7, 8], and it has been implemented in many advanced ultrasound applications, such as shear wave elastography [9], ultrafast micro-vessel imaging [10], and super-resolution ultrasound localization microscopy [11]. However, CPWC images reconstructed using data-independent delay-and-sum (DAS) suffer from a low quality due to broadened mainlobes and granting lobes [12]. In the past several decades, adaptive beamforming has been studied in depth to generate high-quality ultrasound images. Dual apodization with cross-correlation (DAX) [13] uses dual apodization, which is effective in removing clutter, to determine the contributions from the mainlobe and clutter in radio-frequency (RF) signals, and significantly improves the contrast-to-noise ratio (CNR). The minimum variance (MV) beamformer, which was first introduced by [PERSON] [14], can significantly reduce the off-axis interference and sidelobes, and thus it can improve the resolution performance [15; 16]. The eigenspace-based MV (ES-BMV) [17] was then proposed by decomposing echo signals to desired signal and incoherent noise subspaces with the aim to improve the contrast of MV. In addition, short-lag spatial coherence (SLSC) imaging [18], the delay-multiply-and-sum (DMAS) beamformer [19], and the convolutional beamforming algorithm (COBA) [20] have enabled state-of-art image reconstruction with noisy data in ultrasound imaging [21; 22; 23; 24]. Nevertheless, ESBMV, SLSC, DMAS, and COBA tend to introduce dark-region artifacts beside hyperechoic targets in ultrasound imaging [25]. [PERSON] et al. [26] proposed regional-lag signed DMAS for CPWC imaging to overcome the tradeoff between speckle preservation and resolution. In addition, pixel-based adaptive weighting, which enables an enhanced image quality, has also been investigated. The coherence-derived coherence factor (CF) [27] estimates the ratio of coherent energy to incoherent energy and directly weights the DAS beamformed data to reduce sidelobes. It can reduce the effects of phase aberration and reverberation and thus reduce artifacts from weakly coherent off-axis scatter and the granting lobe. However, a major problem of CF is the over-suppression of speckle signals, which leads to degraded speckle statistics with dark-region artifacts and a low speckle intensity. To this end, some promising solutions to overcome this problem have been developed, including generalized CF (GCF) using low-frequency energy [28], scaled CF (scCF) depending on the SNR [29], and spatio-temporally smoothed CF (StS-CF) [30]. These methods can preserve speckle signals to some extent, but possibly at the expense of the resolution advantage of CF. [PERSON] et al. [31] proposed lag-one coherence adaptive normalization (LoSCAN), which is derived from lag-one coherence (LOC) [32] and CF, to suppress incoherent clutter, leading to an improved contrast with no dark-region artifacts. Recently, the amplitude standard deviation (ASD) of echo signals, which can differentiate clutter, has also been studied to suppress clutter. The signal mean-to-standard-deviation factor (SMSF) [33] estimates the ratio of mean and ASD to significantly improve the resolution and contrast.