Research interests

My research is focus in the theory of inverse problems and its applications. As an example of an inverse problem, consider the problem of recovering the acoustic wave speed inside a medium from information measured only at the boundary. If we know the internal wave speed of the medium, given initial and boundary conditions, then the wave equation predicts how acoustic waves propagate in its interior, but could we “ invert” the wave equation as to recover the internal wave speed by controlling only its initial conditions and boundary information? More generally, could we determine what information about the medium is encoded in an acoustic wave when measured at the boundary? In several applications, we want to analyze physical and chemical properties of a model, but we only have access to indirect information of this properties. Inverse Problems deals with recovering such information from a set of accessible data. This area is of substantial and growing interest for disciplines like medical imaging, geophysics, quantum mechanics, astronomy, etc. Many of these mathematical models are described by means of a partial differential equations (PDE). Thus, a typical inverse problem is to recover the coefficients of a PDE (i.e., physical properties like medium propagation, internal density distribution, etc), from measurements on the boundary of the domain, or at infinity. In general, these problems are highly non-linear and ill-posed, demanding tools from different areas of mathematics (e.g., differential geometry, microlocal analysis, functional analysis, etc).

Publications

  • C. Montalto and A. Tamasan, Stability in conductivity imaging from partial measurements of one interior current, Inverse Problems and Imaging, 11 (2017).
  • S. Acosta and C. Montalto, Photoacoustic imaging taking into account thermodynamic attenuation, Inverse Problems, 32 (2016).
  • S. Acosta and C. Montalto, Multiwave imaging in an enclosure with variable sound speed, Inverse Problems 31 (2015). pdf
  • C. Montalto, I. Dorado, D. Aliaga, F. Meng and M. Menezes, A Total Variation Approach for Customizing Imagery to Improve Visual Acuity, ACM Transactions on Graphics 34 (2015) pdf | video
  • C. Montalto, Stable determination of a simple metric, a co-vector field and a potential from the hyperbolic Dirichlet-to-Neumann map, Comm. Partial Differential Equations 39 (2014) pdf
  • C. Montalto and P. Stefanov, Stability of Coupled-Physics Inverse Problems with one Internal Measurement, Inverse Problems 29 (2013) pdf
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