  We present an adaptive imaging technique that optically computes a low-rank
approximation of a scene's hyperspectral image, conceptualized as a matrix.
Central to the proposed technique is the optical implementation of two
measurement operators: a spectrally-coded imager and a spatially-coded
spectrometer. By iterating between the two operators, we show that the top
singular vectors and singular values of a hyperspectral image can be adaptively
and optically computed with only a few iterations. We present an optical design
that uses pupil plane coding for implementing the two operations and show
several compelling results using a lab prototype to demonstrate the
effectiveness of the proposed hyperspectral imager.
