1,471 research outputs found
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
Image restoration using HOS and the Radon transform
The authors propose the use of higher-order statistics (HOS) to study the problem of image restoration. They consider images degraded by linear or zero phase blurring point spread functions (PSF) and additive Gaussian noise. The complexity associated with the combination of two-dimensional signal processing and higher-order statistics is reduced by means of the Radon transform. The projection at each angle is an one-dimensional signal that can be processed by any existing 1-D higher-order statistics-based method. They apply two methods that have proven to attain good one-dimensional signal reconstruction, especially in the presence of noise. After the ideal projections have been estimated, the inverse Radon transform gives the restored image. Simulation results are provided.Peer ReviewedPostprint (published version
Shift-invariant image reconstruction of speckle-degraded using bispectrum estimation
Coherent speckle noise is modeled as a multiplicative noise process that has a negative exponential probability density function. Using a homomorphic transfor mation, this speckle noise is converted to a signal-independent, additive process. The speckled images are randomly jittered from frame-to-frame against a uniform background to simulate image motion and/or platform jitter. Multiple images are logarithmically transformed and ensemble averaged in the bispectral domain. The bispectrum ignores this image motion so no blurring results from the ensemble averaging. Object Fourier magnitude and phase information are also retained in the bispectrum so that the resultant image can be uniquely reconstructed. This value is then exponentiated to complete the image reconstruc tion process. Since speckle masks the resolution of details in the noisy image and effectively destroys the object structure within the image, it is seen that image reconstruction using bispectrum estimation results in images that regain their object structure. Both one-dimensional and two-dimensional images were tested using separate bispectral signal reconstruction algorithms for each
Least-squares Fourier phase estimation from the modulo 2Pi bispectrum phase
The recovery of Fourier phases from measurements of the bispectrum occupies a vital role in many astronomical speckle imaging schemes. In arecent paper [J. Opt. Soc. Am. A 7, 14 (1990)] it was suggested that a least-squares solution to this problem must fail if the bispectrum phase is known only modulo 2Ď€. Here an alternative nonlinear least-squares algorithm is presented that differs from the linear method discussed in the aforementioned paper and that permits the fitting of Fourier phases directly to modulo 2Ď€ measurements of the bispectrum phase, thus eliminating any need for phase unwrapping. Numerical simulations of this method confirm that it is reliable and robust in the presence of noise and verify its enhanced performance when compared with a linear least-squares method that includes the unwrapping of the bispectral phase before Fourier phase retrieval
Oscillations in the bispectrum
There exist several models of inflation that produce primordial bispectra
that contain a large number of oscillations. In this paper we discuss these
models, and aim at finding a method of detecting such bispectra in the data. We
explain how the recently proposed method of mode expansion of bispectra might
be able to reconstruct these spectra from separable basis functions. Extracting
these basis functions from the data might then lead to observational
constraints on these models.Comment: 6 pages, 2 figures, submitted to JOP: Conference Series, PASCOS 201
Bispectrum as Baryon Acoustic Oscillation Interferometer
The galaxy bispectrum, measuring excess clustering of galaxy triplets, offers
a probe of dark energy via baryon acoustic oscillations (BAOs). However up to
now it has been severely underused due to the combinatorically explosive number
of triangles. Here we exploit interference in the bispectrum to identify
triangles that amplify BAOs. This approach reduces the computational cost of
estimating covariance matrices, offers an improvement in BAO constraints
equivalent to lengthening BOSS by 30%, and simplifies adding bispectrum BAO
information to future large-scale redshift survey analyses.Comment: 6 pages, 3 figures; revised to match published versio
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