[T*\,T]=I by a rank-one pr ojection one unveils an accessible spectral analys is classification

with singular integrals of C auchy type as generic examples. An inverse spectra l problem for this class

of (hyponormal) opera tors can be invoked for encoding and decoding (par tial) data of 2D pictures carrying a grey shade fu nction.

An exponential transform\, the two dim ensional analog of a similar operation on Cauchy i ntegrals

introduced by A\, Markov in his pione ering work on 1D moment problems\, provides an eff ective dictionary

between "pictures" in the fr equency domain and "matrices" in the state space i nterpretation.

A natural Riemann-Hilbert probl em lies at the origin of this kernel with potentia l theoretic flavor. Quadrature domains for

ana lytic functions are singled out by a rationality p roperty of the exponential transform\, and hence a n exact reconstruction

algorithm for this clas s of black and white shapes emerges. A two variabl e diagonal Pade approximation scheme and

some related complex orthogonal polynomials enter into the picture\, with their elusive zero asymptotics .

Most of the results streaming from two decad es of joint work with Bjorn Gustafsson.

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