The research in our group is focused on the development and analysis of signal and image processing algorithms for solving what are known as inverse problems. Examples of such problems can be found in fields ranging from image restoration and medical imaging to geophysical exploration and non-destructive testing. Many of the problems in which we are interested are closely related to some underlying physical process such as wave propagation or heat diffusion and our algorithms are designed to incorporate in some reasonable way, the appropriate mathematical models (i.e. the wave equation, the Helmholtz equation, the diffusion equation, etc.).