## 1 Introduction
[24] showed that contrast is improved in the SLSC weighted image, while CNR is slightly reduced as compared to the DAS image. In addition to these coherence-based methods, several new adaptive weighting factors have been identified as enhancing CPWC image quality. To improve image resolution and contrast, a normalized autocorrelation factor (NAF) was proposed for CPWC [25]. [PERSON] et al. [26] introduced a subarray zeros-cross factor (SZF), which was based on the polarity of the adjacent plane-wave imaging results to evaluate signal coherence. SZF can obtain a higher quality of speckle pattern than CF and GCF, with a low computational complexity close to CF. Though adaptive weighting methods can reduce noise and clutter and suppress sidelobes, they tend to suppress the desired signals, especially for signals in the background speckle. It is known that the speckle contains coherent and incoherent components [14]. However, adaptive weighting methods usually reduce the incoherent signals, and thus result in an altered speckle pattern [27]. Singular value decomposition (SVD) is often used to help extract and preserve desired signals from raw signals. SVD has been introduced into Doppler imaging to filter the clutter in echo signals [28; 29; 30]. Recently, SVD was applied to ultrasound imaging to improve image quality. [PERSON] et al. [31] proposed an SVD filter for speckle noise reduction and applied it to monofocal imaging. [PERSON] et al. [32] proposed a sidelobe suppression beamformer based on SVD for CPWC, which can reduce the sidelobe level and improve the contrast-to-noise ratio (CNR). The sidelobe distributions in plane-wave images of different angles were uncorrelated, while the mainlobe energy originating from on-axis targets was highly correlated. Therefore, the utilization of the SVD to filter the beamformed plane-wave RFdata before summation can suppress sidelobes in CPWC. In [PERSON]'s study [32], all beamformed signals from the entire imaging region are reshaped to a matrix; then, the matrix is decomposed by SVD, resulting in enhanced computational efficiency. However, in this approach, the suppression of noise is limited. While the adaptive weighting methods are excellent at noise reduction so as to address these limitations. Inspired by these findings, we proposed a neighborhood SVD (NSVD) filter for CPWC that computes the SVD in a neighboring region to obtain high-quality images. We applied the NSVD filter to adaptive beamforming to achieve both noise reduction and speckle pattern preservation. For a point \(p\) in a plane-wave image, we selected a rectangular neighbor region centered around point \(p\) to form a two-dimensional matrix. Then, a three-dimensional data matrix is obtained and reshaped to rebuild a matrix with two dimensions representing samples and plane-waves with different steering angles, respectively. SVD is performed on this two-dimensional matrix to complete decomposition and reconstruction. Finally, the compound output of the imaging point \(p\) can be obtained through the summation of the filtered plane-wave images. We present a sliding rectangular window with a fixed size to perform the procedure for every imaging point and filter the entire imaging region. The proposed NSVD filter was then combined with adaptive weighting methods to enhance noise reduction and preserve the speckle pattern. SVD was recently used in a speckle-tracking algorithm to reduce the effect of clutter and noise of stationary background for quantifying displacement in the carpal tunnel [33]. In this paper, we used the NSVD filter to extract effective signals for all steering plane-wave imaging results. Then, the extracted signals were used to estimate adaptive weighting factors and reconstruct images. With this application of NSVD, adaptive weighting methods can achieve improvements in contrast and speckle pattern preservation. We used CF, GCF, and SLSC combined with NSVD to verify the performance for image quality enhancement.