  One of a key problems in signal reconstruction process with the use of frames
is to find a dual frame. Typically, a canonical dual frame is used. However,
there are many applications where this choice appears to be unfortunate. Due to
that fact, it is necessary to develop a tool, which helps to find a suitable
dual frame. In this paper we give a method to find every dual frames. The
proposed method is based on Naimark's dilation theorem and the obtained
description of dual frames involves parameters that characterize extension of a
Parseval frame to an orthonormal basis. These formulas are simplified for
frames in finite-dimensional spaces and for near-Riesz bases. In the latter
case, the simplification is based on the extended and supplemented version of
the Naimark theorem, which is proved in the last part of the paper.
