  This paper presents two novel regularization methods motivated in part by the
geometric significance of biorthogonal bases in signal processing applications.
These methods, in particular, draw upon the structural relevance of
orthogonality and biorthogonality principles and are presented from the
perspectives of signal processing, convex programming, continuation methods and
nonlinear projection operators. Each method is specifically endowed with either
a homotopy or tuning parameter to facilitate tradeoff analysis between accuracy
and numerical stability. An example involving a basis comprised of real
exponential signals illustrates the utility of the proposed methods on an
ill-conditioned inverse problem and the results are compared to standard
regularization techniques from the signal processing literature.
