Non-local image deconvolution by Cauchy sequence

We present the deconvolution between two smooth function vectors as a Cauchy sequence of weight functions. From this we develop a Taylor series expansion of the convolution problem that leads to a non-local approximation for the deconvolution in terms of continuous function spaces. Optimisation of this form against a given measure of error produces a theoretically more exact algorithm. The discretization of this formulation provides a deconvolution iteration that deconvolves images quicker than the Richardson-Lucy algorithm.Comment: 12 pages, 3 figure

Independent component analysis applications in CDMA systems

Thesis (Master)--Izmir Institute of Technology, Electronics and Communication Engineering, Izmir, 2004Includes bibliographical references (leaves: 56)Text in English; Abstract: Turkish and Englishxi, 96 leavesBlind source separation (BSS) methods, independent component analysis (ICA) and independent factor analysis (IFA) are used for detecting the signal coming to a mobile user which is subject to multiple access interference in a CDMA downlink communication. When CDMA models are studied for different channel characteristics, it is seen that they are similar with BSS/ICA models. It is also showed that if ICA is applied to these CDMA models, desired user.s signal can be estimated successfully without channel information and other users. code sequences. ICA detector is compared with matched filter detector and other conventional detectors using simulation results and it is seen that ICA has some advantages over the other methods.The other BSS method, IFA is applied to basic CDMA downlink model. Since IFA has some convergence and speed problems when the number of sources is large, firstly basic CDMA model with ideal channel assumption is used in IFA application.With simulation of ideal CDMA channel, IFA is compared with ICA and matched filter.Furthermore, Pearson System-based ICA (PS-ICA) method is used forestimating non-Gaussian multipath fading channel coefficients. Considering some fading channel measurements showing that the fading channel coefficients may have an impulsive nature, these coefficients are modeled with an -stable distribution whose shape parameter takes values close to 2 which makes the distributions slightly impulsive. Simulation results are obtained to compare PS-ICA with classical ICA.Also IFA is applied to the single path CDMA downlink model to estimate fading channel by using the advantage of IFA which is the capability to estimate sources with wide class of distributions

Subspace-based channel estimation for DS/CDMA systems exploiting pulse- shaping information.

Thesis (M.Sc.Eng.)-University of Natal, Durban, 2003.Third generation wireless systems have adopted Direct-Sequence/Code-Division Multiple-Access (DS/CDMA) as the multiple access scheme of communication. This system would typically operate in a multipath fading channel. This dissertation only deals with the task of channel estimation at the base station where the multipath delays and attenuations for each user are estimated. This information is used to aid the recovery of data that was transmitted by each user. Subspace-based algorithms are popularly used to perform the task of channel estimation because they have the desirable property of perfectly estimating the channel in a noise-free environment. In this dissertation a new subspace-based channel estimation algorithm for DS/CDMA systems is presented. The proposed algorithm is based on the Parametric Subspace algorithm by Perros-Meilhac et al. for single-user systems. The main focus of this dissertation is to convert the Parametric Subspace algorithm from a single-user system to a multi-user DS/CDMA system. It has been shown in the literature that by using information of the pulse-shaping filter in the Channel Subspace algorithm, the variance of the channel estimates is decreased. However, this has only been applied to a single-user system. There are several subspace algorithms that have been proposed for DS/CDMA systems. Most of these algorithms sample the received signal at the chip rate, making it impossible to exploit knowledge of the pulse-shaping filter in the channel estimation algorithm. In this dissertation a new subspace-based channel estimation algorithm is derived for a DS/CDMA system with multiple receive antennas, where the output is oversampled with respect to the chip rate. By oversampling the received signal, knowledge of the pulse-shaping filter is used in the channel estimation algorithm. It is shown that the variance of the channel estimate for the proposed subspace algorithm is less than the Torlak/Xu subspace algorithm that does not exploit information of the pulse-shaping filter. A mathematical expression of the mean square error of estimation for the new algorithm is also derived. It was shown that the analytic expression provides a good approximation of the actual MSE for high SNR. The Parametric Subspace Delay Estimation (PSDE) algorithm was developed by Perros-Meilhac et al. to estimate the multipath delays introduced by the communications channel. The limitation of the PSDE algorithm is that the performance of the algorithm deteriorates as the power of the multipath signals decrease with increasing delay time. This dissertation proposes a modified version of the PSDE algorithm, called the Modified Parametric Subspace Delay Estimation (MPSDE) algorithm, which performs better than the PSDE algorithm in an environment where the power of the multipath signals varies. The final part of this dissertation discusses the Torlak/Xu channel estimation algorithm and the Bensley/Aazbang delay estimation algorithm. In order to compare the performance of these two subspace algorithms, the Torlak/Xu algorithm is converted to a delay estimation algorithm that is called the Parametric TX algorithm. The performance of the Bensley/Aazbang delay estimation algorithm and the proposed Parametric TX algorithm are compared and it is shown that the Parametric TX algorithm offers the better performance

On Partial and Generic Uniqueness of Block Term Tensor Decomposition in Signal Processing

In this dissertation, we study the partial and generic uniqueness of block term tensor decompositions in signal processing. We present several conditions for generic uniqueness of tensor decompositions of multilinear rank (1, L1, L1), ..., (1, LR, LR) terms. Our proof is based on algebraic geometric methods. Mathematical preliminaries for this dissertation are multilinear algebra, and classical algebraic geometry. In geometric language, we prove that the joins of relevant subspace varieties are not tangentially weakly defective. We also give conditions for partial uniqueness of block term tensor decompositions by proving that the joins of relevant subspace varieties are not defective. The main result is the following. For a tensor Y belong to the tensor product of three complex vector spaces of dimensions I, J, K, we assume that L1, L2, ..., LR is from small to large, K is bigger or equal to J, and J is strictly bigger than LR. If the dimension of ambient space is strictly less than IJK, then for general tensors among those admitting block term tensor decomposition, the block term tensor decomposition is partially unique under the condition that the binomial coefficient indexed by J and LR is bigger or equal to R, and I is bigger or equal to 2; it has infinitely many expressions under the condition IJK is strictly less than the sum from L_1^2 to L_R^2; it is essentially unique under any of the following there conditions: (i) I is bigger or equal to 2, J, K is bigger or equal to the sum from L1 to LR (ii) R is 2, I is bigger or equal to 2 (iii) I is bigger or equal to R, K is bigger or equal to the sum from L1 to LR, J is bigger or equal to 2LR, the binomial coefficient indexed by J and LR is bigger or equal to R