Objective. A phased or a curvilinear array produces ultrasound (US) images with a sector field of view (FOV), which inherently exhibits spatially-varying image resolution with inferior quality in the far zone and towards the two sides azimuthally. Sector US images with improved spatial resolutions are favorable for accurate quantitative analysis of large and dynamic organs, such as the heart. Therefore, this study aims to translate US images with spatially-varying resolution to ones with less spatially-varying resolution. CycleGAN has been a prominent choice for unpaired medical image translation; however, it neither guarantees structural consistency nor preserves backscattering patterns between input and generated images for unpaired US images. Approach. To circumvent this limitation, we propose a constrained CycleGAN (CCycleGAN), which directly performs US image generation with unpaired images acquired by different ultrasound array probes. In addition to conventional adversarial and cycle-consistency losses of CycleGAN, CCycleGAN introduces an identical loss and a correlation coefficient loss based on intrinsic US backscattered signal properties to constrain structural consistency and backscattering patterns, respectively. Instead of post-processed B-mode images, CCycleGAN uses envelope data directly obtained from beamformed radio-frequency signals without any other non-linear postprocessing. Main Results. In vitro phantom results demonstrate that CCycleGAN successfully generates images with improved spatial resolution as well as higher peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) compared with benchmarks. Significance. CCycleGAN-generated US images of the in vivo human beating heart further facilitate higher quality heart wall motion estimation than benchmarks-generated ones, particularly in deep regions.