Browsing by Subject "Signal recovery"

Now showing 1 - 6 of 6

Open Access
Average error in recovery of sparse signals and discrete fourier transform
(IEEE, 2012-04) Özçelikkale, Ayça; Yüksel, S.; Özaktaş Haldun M.
In compressive sensing framework it has been shown that a sparse signal can be successfully recovered from a few random measurements. The Discrete Fourier Transform (DFT) is one of the transforms that provide the best performance guarantees regardless of which components of the signal are nonzero. This result is based on the performance criterion of signal recovery with high probability. Whether the DFT is the optimum transform under average error criterion, instead of high probability criterion, has not been investigated. Here we consider this optimization problem. For this purpose, we model the signal as a random process, and propose a model where the covariance matrix of the signal is used as a measure of sparsity. We show that the DFT is, in general, not optimal despite numerous results that suggest otherwise. © 2012 IEEE.
Open Access
The effect of distribution of information on recovery of propagating signals
(2015-09) Karabulut, Özgecan
Interpolation is one of the fundamental concepts in signal processing. The analysis of the di fficulty of interpolation of propagating waves is the subject of this thesis. It is known that the information contained in a propagating wave fi eld can be fully described by its uniform samples taken on a planar surface transversal to the propagation direction, so the eld can be found anywhere in space by using the wave propagation equations. However in some cases, the sample locations may be irregular and/or nonuniform. We are concerned with interpolation from such samples. To be able to reduce the problem to a pure mathematical form, the fractional Fourier transform is used thanks to the direct analogy between wave propagation and fractional Fourier transformation. The linear relationship between each sample and the unknown field distribution is established this way. These relationships, which constitute a signal recovery problem based on multiple partial fractional Fourier transform information, are analyzed. Recoverability of the fi eld is examined by comparing the condition numbers of the constructed matrices corresponding to di fferent distributions of the available samples.
Open Access
Generalized filtering configurations with applications in digital and optical signal and image processing
(1999) Kutay, Mehmet Alper
In this thesis, we first give a brief summary of the fractional Fourier transform which is the generalization of the ordinary Fourier transform, discuss its importance in optical and digital signal processing and its relation to time-frequency representations. We then introduce the concept of filtering circuits in fractional Fourier domains. This concept unifies the multi-stage (repeated) and multi-channel (parallel) filtering configurations which are in turn generalizations of single domain filtering in fractional Fourier domains. We show that these filtering configurations allow a cost-accuracy tradeoff by adjusting the number of stages or channels. We then consider the application of these configurations to three important problems, namely system synthesis, signal synthesis, and signal recovery, in optical and digital signal processing. In the system and signal synthesis problems, we try to synthesize a desired system characterized by its kernel, or a desired signal characterized by its second order statistics by using fractional Fourier domain filtering circuits. In the signal recovery problem, we try to recover or estimate a desired signal from its degraded version. In all of the examples we give, significant improvements in performance are obtained with respect to single domain filtering methods with only modest increases in optical or digital implementation costs. Similarly, when the proposed method is compared with the direct implementation of general linear systems, we see that significant computational savings are obtained with acceptable decreases in performance.
Open Access
Resolution enhancement of low resolution wavefields with POCS algorithm
(The Institution of Engineering and Technology, 2003) Çetin, A. Enis; Özaktaş, H.; Özaktaş, Haldun M.
The problem of enhancing the resolution of wavefield or beam profile measurements obtained using low resolution sensors is addressed by solving the problem of interpolating signals from partial fractional Fourier transform information in several domains. The iterative interpolation algorithm employed is based on the method of projections onto convex sets (POCS).
Open Access
Signal recovery from partial fractional fourier transform information
(IEEE, 2004) Çetin, A. Enis; Özaktaş, H.; Özaktaş, Haldun M.
The fractional Fourier transform has found many applications in signal and image processing and optics. An iterative algorithm for signal recovery from partial fractional Fourier transform information is presented. The signal recovery algorithm is constructed by using the method of projections onto convex sets and convergence of the algorithm is assured.
Open Access
Signal recovery from wavelet transform maxima
(IEEE, 1994-01) Çetin, A. Enis; Ansari, R.
This paper presents an iterative algorithm for signal recovery from discrete-time wavelet transform maxima. The signal recovery algorithm is developed by using the method of projections onto convex sets. Convergence of the algorithm is assured.