We analyze the principles underlying minimum variance distortionless response (MVDR) beamforming in order to integrate it into a pixel-based algorithm. There is a challenge posed by the low echo signal-to-noise ratio (eSNR) when calculating beamformer contributions at pixels far away from the beam centreline. Together with the well-known scarcity of samples for covariance matrix estimation, this reduces the beamformer performance and degrades the image quality. To address this challenge, we implement the MVDR algorithm in two different ways. First, we develop the conventional minimum variance pixel-based (MVPB) beamformer that performs the MVDR after the pixel-based superposition step. This involves a combination of methods in the literature, extended over multiple transmits to increase the eSNR. Then we propose the coherent MVPB beamformer, where the MVDR is applied to data within individual transmits. Based on pressure field analysis, we develop new algorithms to improve the data alignment and matrix estimation, and hence overcome the low-eSNR issue. The methods are demonstrated on data acquired with an ultrasound open platform. The results show the coherent MVPB beamformer substantially outperforms the conventional MVPB in a series of experiments, including phantom and in vivo studies. Compared to the unified pixel-based beamformer, the newest delay-and-sum algorithm in [1], the coherent MVPB performs well on regions that conform to the diffuse scattering assumptions on which the minimum variance principles are based. It produces less good results for parts of the image that are dominated by specular reflections.