We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) Lp or Lp,q (1 ≤ p <∞) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulae allows us to prove some James-type results for atomic decompositions: an uncon...

This paper uses a method for shape reconstruction of a 2-D homogeneous object with arbitrary geometry and known electrical properties. In this method, the object is illuminated by a Gaussian pulse, modulated with sinusoidal carrier plane wave and the time domains’ footprint signal due to object presence is used for the shape reconstruction. A nonlinear feedback loop is used to minimize the diff...

In this paper, we develop a set of conditions under which a sequence is uniquely specified by the phase or samples of the phase of its Fourier transform. These conditions are applicable to mixedphase one-dimensional and multi-dimensional sequences. Under the specified conditions, we also present several algorithms which may be used to reconstruct a sequence from its phase.

An axiomatic approach to signal reconstruction is formulated, involving a sample consistent set and a guiding set, describing desired reconstructions. New frame-less reconstruction methods are proposed, based on a novel concept of a reconstruction set, defined as a shortest pathway between the sample consistent set and the guiding set. Existence and uniqueness of the reconstruction set are inve...

This report will use, in order to measure the performance of a (mathematical) system, the L norm for systems. For a BIBO-stable (Bounded Input Bounded Output) and Linear Continuous Time Invariant (LCTI) system usually a transfer function is defined. Using this transfer function it is possible to calculate the L norm of the system. In the process of sampling and reconstruction of a signal two sy...