Imaging techniques in science, engineering and medicine have evolved to expand our ability to visualize the internal information in an object such as the human body. Examples may include X-ray computed tomography (CT), magnetic resonance imaging (MRI), ultrasound imaging and positron emission tomography (PET). They provide cross-sectional images of the human body, which are solutions of corresponding inverse problems. Information embedded in such an image depends on the underlying physical principle, which is described in its forward problem. Since each imaging modality has limited viewing capability, there have been numerous research efforts to develop new techniques producing additional contrast information not available from existing methods. There are such imaging techniques of practical significance, which can be formulated as nonlinear inverse problems. Electrical impedance tomography (EIT), magnetic induction tomography (MIT), diffuse optical tomography (DOT), magnetic resonance electrical impedance tomography (MREIT), magnetic resonance electrical property tomography (MREPT), magnetic resonance elastography (MRE), electrical source imaging and others have been developed and adopted in application areas where new contrast information is in demand. Unlike X-ray CT, MRI and PET, they manifest some nonlinearity, which
results in their image reconstruction processes being represented by nonlinear inverse problems. Visualizing new contrast information on the electrical, optical and mechanical properties of materials inside an object will widen the applications of imaging methods in medicine, biotechnology, non-destructive testing, geophysical exploration, monitoring of industrial processes and other areas. Some are advantageous in terms of non-invasiveness, portability, convenience of use, high temporal resolution, choice of dimensional scale and total cost. Others may offer a higher spatial resolution, sacrificing some of these merits. Owing primarily to nonlinearity and low sensitivity, in addition to the lack of sufficient information to solve an inverse problem in general, these nonlinear inverse problems share the technical difficulties of ill-posedness, which may result in images with a low spatial resolution. Deep understanding of the underlying physical phenomena as well as the implementation details of image reconstruction algorithms are prerequisites for finding solutions with practical significance and value.