Proc. SPIE. 5562, Image Reconstruction from Incomplete Data III
KEYWORDS: Atrial fibrillation, Data modeling, Error analysis, Tomography, Phase retrieval, Signal processing, Near field diffraction, Computed tomography, Reconstruction algorithms, Wigner distribution functions
The problem of signal recovery from incomplete data is
investigated in the context of phase-space tomography. Particular
emphasis is given to the case where only a limited number
intensity measurements can be performed, which corresponds to
partial coverage of the ambiguity function of the signal. Based on
numerical simulations the impact of incomplete knowledge of the
ambiguity function on the performance of phase-space tomography is
illustrated. Several schemes to address the limited data problem
are evaluated. This includes the use of prior information about
the phase retrieval problem. In addition, the redundancy of
phase-space representations is investigated as the means to
recover the signal from partial knowledge of phase space. A
generalization of deterministic phase retrieval is introduced
which allows one to obtain a model based phase estimate for
bandlimited functions. This allows one to use prior information
for improving the phase estimate in the presence of noise.
We describe an automated target tracking algorithm which is based on a linear spectral estimation technique, termed the PDFT algorithm. Typically, the PDFT algorithm is applied to obtain high resolution images from scattered field data by incorporating prior information about the target shape into the reconstruction process. In this investigation, the algorithm is used iteratively for determining the target location and a target signature which can be used as the input to an automated target recognition systems. The implementation and the evaluation of the algorithm is discussed in the context of low resolution imaging systems with special reference to foliage penetration radar and ground penetrating radar.
For weakly scattering permittivities, each measurement of the scattered far field can be interpreted as a sampling point of the Fourier transformation of the object. Furthermore, each sampling point can be accessed by more than one combination of wavelength, propagation direction, and polarization of the incident field. This means, a set of measurements which access the same sampling point can be regarded as being redundant. For strongly scattering objects the Fourier diffraction slice theorem does not apply. We show that measurements which are redundant in the weakly scattering case can be exploited to resolve difficulties associated with imaging of the strongly scattering objects. One dimensional geometries are investigated to estimate the potential redundant data sets offer for addressing the inverse scattering problem of strongly and multiply scattering objects. In addition, we discuss preliminary results for solving 2D imaging problems.
The limits of ray optical methods to provide a valid model for describing the propagation of electromagnetic radiation are explored. We briefly review fundamentals of ray optics as well as
various extensions. This review is partially intended to emphasize that existing ray based methods are able to address most, if not all, wave phenomena. In addition, we propose an
extension of ray optics which interprets rays as generalized trajectories in an abstract configuration state. This allows us to propose the use of rays and ray optics as fundamental and practical concept to compute any wave phenomenon, including rigorous diffraction problems. Wave optics, in this context, becomes a convenient and efficient method to calculate the ray transfer properties. In addition, our concept facilitates
interfacing conventional ray-tracing methods with wave optical methods to predict diffraction.