Phase unwrapping algorithms play an important role in noncontact optical profilometries such as phase-measuring profilometry. The depth information of the measured object is implicitly defined by certain trigonometric equations derived from image data. The direct solutions to the equations, called the wrapped phases, have a limited range from -\pi to \pi. The main computational problem is to unwrap the wrapped phases over the entire image. This phase unwrapping process is often hindered by the presence of noises, spots of low intensity modulation, and instability of the solutions. We present a novel approach to the problem by formulating the phase solving and unwrapping as an ill-posed problem. By using the regularization method, we will be able to provide a unified view to address various challenges in the problem. A new fully automated algorithm for phase unwrapping based on this approach is also presented.