Many problems in science and engineering are inverse problems. In science, an experimental result that requires an explanation asks the question – given the data, what is the theory/model that provides it? In engineering, a given function (in a product/software …. ) requires a design that provides the function. In cognitive neuroscience, one asks how one can detect, classify and recognize the distal origin of signals from their proximal sensory cues, converting well known forward problems in the physical sciences and engineering, e.g. optics, hydrodynamics and acoustics to inverse problems in psychophysics associated with vision, olfaction, and audition.
Inverse problems are often defined by a goal to be achieved subject to some constraints (such as adherence to physical law, robustness to noise, symmetry), and are usually not well-posed, i.e. they can lead to multiple answers. Our interests in this area span both methodological and practical aspects. In methodology, a recent interest is in statistical-geometric inverse problems from perceptual psychology and cognition. And from a practical perspective, we have worked on a diverse range of applications that include structural optimization, strategies for 3d and 4d printing, optimal drug treatment protocols for protein misfolding diseases, efficient locomotion etc.