IPRPI & RPI Logos Inverse Problems Center

Shear wave speed image of breast cancer with human subject data obtained from Mathias Fink's laboratory. The image was created using the arrival time algorithm.



Reconstruction of shear stiffness due to a breast cancerous tumor from in vivo human subject data.



Approximate P-Wave Speed map in the earthquake active region near Parkfield, CA.



MEMS record soil displacement to enable judgement of embankment integrity



Shear stiffness prostate cancer image correlated with histology slide. Data is in Vitro.



Liver stiffness from MR generated displacement in Vivo data.



Elastic shear modulus reconstruction from tissue-mimicking phantom data using MR generated displacement data.







About us

Tackling Some of Science's Toughest Challenges – In Reverse
At first glance, the following tasks may not seem that similar:

  • Detecting cancer in its early stages
  • Understanding earthquakes
  • Locating objects in a cluttered environment

But a unique center unites researchers who undertake these problems and more, using a common method of research – inverse theory.

The Inverse Problems Center at Rensselaer Polytechnic Institute (IPRPI) has drawn together an interdisciplinary group of researchers with a common interest in dealing with such critical issues – all using inverse theory.

IPRPI at Rensselaer
The field of inverse problems is a vast scientific area in which Rensselaer has a significant, high-quality, well-established scientific base.

IPRPI comprises distinguished researchers in such varied fields as:

  • Mathematics
  • Geosciences
  • Mechanical Engineering
  • Civil Engineering
  • Electrical Engineering

A broad range of application areas are being addressed by IPRPI, including:

  • Geophysics
  • Medical imaging
  • Synthetic aperture radar
  • Ocean acoustics

The impact of IPRPI will also reach far through members' development of specialized software and publications that are shared with the international inverse problems community.

How inverse theory works
With inverse problems, scientists observe an effect and work to determine the cause; the ultimate goal is to find objects and/or their material or biological properties that cannot be directly measured.

In this exciting field, scientific challenges include:

  • Modeling of the physical problem
  • Creating new mathematics for analysis of the model
  • Identifying appropriate (often large) and/or rich data sets
  • Working with scientific computations and visualization aids
  • Undertaking experimental verification

Most approaches are based on effective use of mathematical models in order to make optimal use of the data; an essential part of the problem solution is the use of the mathematical model for the physical process that produces the data.

Since inverse problems are concerned with the processing of data and extraction of relevant information, the field is considered part of Information Technology and Data Science.

Among those problems addressed within IPRPI:
Some are at the most basic scientific level:

  • Finding properties of the earth's substructure from seismic measurements
  • Determining material properties of mechanical or biological systems

Other problems focus on direct applications:

  • Finding tumors in biological tissue
  • Locating sources of heart malfunction distinguishing abnormal from normal tissue
  • Identifying fault locations in earthquake active regions
  • Establishing the integrity of dikes
  • Locating objects concealed by vegetation cover
  • Locating mines in the sea environment

In all these cases, it is either not possible or not desirable to make direct measurements.

Research presentation and discussion to postdocs and graduate students

A great community
Dr. Joyce McLaughlin, a distinguished inverse problems expert, directs the IPRPI center.

A well-known national and international lecturer, McLaughlin has assembled an outstanding team of Rensselaer faculty with interests in a variety of scientific challenges that are investigated using inverse problems.

Among them are journal editors, members of national and international committees, and other noted researchers with extensive international experience.

The community of inverse problems researchers is an international one; therefore, the center aims to recruit visitors and establish exchanges of young researchers from Europe, Australia, Japan, India, and China to participate in IPRPI activities.

An active Center
IPRPI is an active center that provides a global focal point for the inverse problems community.

Ongoing activities include:

  • A semester-long seminar
  • Workshops and conferences featuring prominent guest speakers from Rensselaer and other outstanding academic institutions
  • Collaboration with long-term visitors and academic and industrial colleagues

A major goal
A major goal of IPRPI is to offer strong early career opportunities for:

  • Students
  • Postdoctoral researchers
  • Young faculty members throughout the center

The objectives of this educational component are to advance the scientific health of the discipline, as well as to contribute to the renewal of the scientific/engineering workforce engaged in this cutting edge research.

Current funding
Funding is provided by:

  • National Science Foundation
  • National Institutes of Health
  • Office of Naval Research
  • Air Force Office of Scientific Research

Contact us
For more information on the Inverse Problems Center at Rensselaer Polytechnic Institute, please contact a member of our staff:

Jackie Cortese, IPRPI Assistant
(518) 276-2145
(518) 276-4824 (fax)

Dr. Joyce McLaughlin, IPRPI Director
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, N.Y. 12180 USA
(518) 276-6349


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