The visual quality of ultrasound (US) images is crucial for clinical diagnosis and treatment. The main source of image quality degradation is the inherent speckle noise generated during US image acquisition. Current deep learning-based methods cannot preserve the maximum boundary contrast when removing noise and speckle. In this paper, we address the issue by proposing a novel wavelet-based generative adversarial network (GAN) for real-time high-quality US image reconstruction, viz. WGAN-DUS. First, we propose a batch normalization module (BNM) to balance the importance of each sub-band image and fuse sub-band features simultaneously. Then, a wavelet reconstruction module (WRM) integrated with a cascade of wavelet residual channel attention block (WRCAB) is proposed to extract distinctive sub-band features used to reconstruct denoised images. A gradual tuning strategy is proposed to fine-tune our generator for better despeckling performance. We further propose a wavelet-based discriminator and a comprehensive loss function to effectively suppress speckle noise and preserve the image features. Besides, we have designed an algorithm to estimate the noise levels during despeckling of real US images. The performance of our network was then evaluated on natural, synthetic, simulated and clinical US images and compared against various despeckling methods. To verify the feasibility of WGAN-DUS, we further extend our work to uterine fibroid segmentation with the denoised US image of the proposed approach. Experimental result demonstrates that our proposed method is feasible and can be generalized to clinical applications for despeckling of US images in real-time without losing its fine details.