Dear Colleagues,

The term “inverse problem” is quite general, and in principal an “inverse problem” appears whenever we seek to invert a mapping between two sets. However, within the field of inverse problems the two sets are normally function spaces and the mapping to be inverted involves the solution of some partial differential equations (PDEs). Well-known examples include the mapping from a conductivity to the Dirichlet-to-Neumann map in the so-called Calderón problem and the mapping from density to attenuation in computerized tomography. Both theoretical and practical questions arise when studying inverse problems. On the theoretical side we may ask if the inverse problem is well-posed in the sense of Hadamard: a continuous inverse mapping exists and is unique. On the practical side we may seek algorithms to calculate the inverse mapping.

Geometric structure appears naturally in many inverse problems because of the symmetries of the PDEs involved. For example, if we allow the conductivity to be anisotropic in Calderón’s problem then the solution of the inverse problem becomes non-unique because the structure of the PDE is preserved by diffeomorphism. Indeed, non-uniqueness in many inverse problems arises as a result of an invariance of the underlying PDE, which leads us to consider differential geometry.

This Special Issue will accept high-quality papers with original research which combines inverse problems and differential geometry.

Dr. Sean Holman
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• inverse problems
• differential geometry
• tomography
• parameter identification