Generative Adversarial Networks (GANs) are considered the state-of-the-art in the field of image generation. They learn the joint distribution of the training data and attempt to generate new data samples in high dimensional space following the same distribution as the input. Recent improvements in GANs opened the field to many other computer vision applications based on improving and changing the characteristics of the input image to follow some given training requirements. In this paper, we propose a novel technique for the denoising and reconstruction of the micro-Doppler ($\boldsymbol{\mu}$-D) spectra of walking humans based on GANs. Two sets of experiments were collected on 22 subjects walking on a treadmill at an intermediate velocity using a \unit[25]{GHz} CW radar. In one set, a clean $\boldsymbol{\mu}$-D spectrum is collected for each subject by placing the radar at a close distance to the subject. In the other set, variations are introduced in the experiment setup to introduce different noise and clutter effects on the spectrum by changing the distance and placing reflective objects between the radar and the target. Synthetic paired noisy and noise-free spectra were used for training, while validation was carried out on the real noisy measured data. Finally, qualitative and quantitative comparison with other classical radar denoising approaches in the literature demonstrated the proposed GANs framework is better and more robust to different noise levels.