Improved techniques for bispectral reconstruction of signals

Higher order cumulants and spectra have found a variety of uses in many areas of digital signal processing. The third order spectrum, or bispectrum, is of specific interest to researchers because of some of its properties. The Bispectrum is defined as the fourier transform of the third order cumulant se quence for stochastic processes, and as a triple product of fourier transforms for deterministic signals. In the past, bispectral analysis has been used in applications such as identification of linear filters, quadratic phase coupling problems and detection of deviations from normality. This work is aimed at developing techniques for reconstructing deterministic signals in noise us ing the bispectrum. The bispectrum is zero for many noise processes, and is insensitive to linear phase shifts. The main motivation of this work is to exploit these properties of bispectrum that are potentially useful in signal re covery. The existing bispectral recovery techniques are discussed in the signal reconstruction frame work and their main limitation in handling noisy de terministic signals is brought out. New robust reconstruction procedures are provided in order to use bispectrum in such cases. The developed algorithms are tested over a range of simulated applications to bring out their robustness in handling both deterministic and stochastic signals. The new techniques are compared with existing bispectral methods in various problems. This thesis also discusses some of the tradeoffs involved in using bispectrum based reconstruction approaches against non-bispectral methods

PyHST2: an hybrid distributed code for high speed tomographic reconstruction with iterative reconstruction and a priori knowledge capabilities

We present the PyHST2 code which is in service at ESRF for phase-contrast and absorption tomography. This code has been engineered to sustain the high data flow typical of the third generation synchrotron facilities (10 terabytes per experiment) by adopting a distributed and pipelined architecture. The code implements, beside a default filtered backprojection reconstruction, iterative reconstruction techniques with a-priori knowledge. These latter are used to improve the reconstruction quality or in order to reduce the required data volume and reach a given quality goal. The implemented a-priori knowledge techniques are based on the total variation penalisation and a new recently found convex functional which is based on overlapping patches. We give details of the different methods and their implementations while the code is distributed under free license. We provide methods for estimating, in the absence of ground-truth data, the optimal parameters values for a-priori techniques

Phase retrieval with polarization

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a novel measurement design which is inspired by interferometry and exploits certain properties of expander graphs. We also give an efficient phase retrieval procedure, and use recent results in spectral graph theory to produce a stable performance guarantee which rivals the guarantee for PhaseLift in [Candes et al. 2011]. We use numerical simulations to illustrate the performance of our phase retrieval procedure, and we compare reconstruction error and runtime with a common alternating-projections-type procedure