A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

SCSA based MATLAB pre-processing toolbox for 1H MR spectroscopic water suppression and denoising

In vivo 1H Magnetic Resonance Spectroscopy (MRS) is a useful tool in assessing neurological and metabolic disease, and to improve tumor treatment. Different pre-processing pipelines have been developed to obtain optimal results from the acquired data with sophisticated data fitting, peak suppression, and denoising protocols. We introduce a Semi-Classical Signal Analysis (SCSA) based Spectroscopy pre-processing toolbox for water suppression and data denoising, which allows researchers to perform water suppression using SCSA with phase correction and apodization filters and denoising of MRS data, and data fitting has been included as an additional feature, but it is not the main aim of the work. The fitting module can be passed on to other software. The toolbox is easy to install and to use: 1) import water unsuppressed MRS data acquired in Siemens, Philips and .mat file format and allow visualization of spectroscopy data, 2) allow pre-processing of single voxel and multi-voxel spectra, 3) perform water suppression and denoising using SCSA, 4) incorporate iterative nonlinear least squares fitting as an extra feature. This article provides information about how the above features have been included, along with details of the graphical user interface using these features in MATLAB

1 A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Abstract—Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured “noises”. As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data. Index Terms—Convex optimization, Parallel algorithms, Wavelet transforms, Adaptive filters, Geophysical signal processing, Signal restoration, Sparsity, Signal separation

Novel methods in image halftoning

Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Science, Bilkent Univ., 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 97-101Halftoning refers to the problem of rendering continuous-tone (contone) images on display and printing devices which are capable of reproducing only a limited number of colors. A new adaptive halftoning method using the adaptive QR- RLS algorithm is developed for error diffusion which is one of the halftoning techniques. Also, a diagonal scanning strategy to exploit the human visual system properties in processing the image is proposed. Simulation results on color images demonstrate the superior quality of the new method compared to the existing methods. Another problem studied in this thesis is inverse halftoning which is the problem of recovering a contone image from a given halftoned image. A novel inverse halftoning method is developed for restoring a contone image from the halftoned image. A set theoretic formulation is used where sets are defined using the prior information about the problem. A new space domain projection is introduced assuming the halftoning is performed ,with error diffusion, and the error diffusion filter kernel is known. The space domain, frequency domain, and space-scale domain projections are used alternately to obtain a feasible solution for the inverse halftoning problem which does not have a unique solution. Simulation results for both grayscale and color images give good results, and demonstrate the effectiveness of the proposed inverse halftoning method.Bozkurt, GözdeM.S

Optimal design of magnitude responses of rational infinite impulse response filters

This correspondence considers a design of magnitude responses of optimal rational infinite impulse response (IIR) filters. The design problem is formulated as an optimization problem in which a total weighted absolute error in the passband and stopband of the filters (the error function reflects a ripple square magnitude) is minimized subject to the specification on this weighted absolute error function defined in the corresponding passband and stopband, as well as the stability condition. Since the cost function is nonsmooth and nonconvex, while the constraints are continuous, this kind of optimization problem is a nonsmooth nonconvex continuous functional constrained problem. To address this issue, our previous proposed constraint transcription method is applied to transform the continuous functional constraints to equality constraints. Then the nonsmooth problem is approximated by a sequence of smooth problems and solved via a hybrid global optimization method. The solutions obtained from these smooth problems converge to the global optimal solution of the original optimization problem. Hence, small transition bandwidth filters can be obtained

Wavelet-based digital image restoration

Digital image restoration is a fundamental image processing problem with underlying physical motivations. A digital imaging system is unable to generate a continuum of ideal pointwise measurements of the input scene. Instead, the acquired digital image is an array of measured values. Generally, algorithms can be developed to remove a significant part of the error associated with these measure image values provided a proper model of the image acquisition system is used as the basis for the algorithm development. The continuous/discrete/continuous (C/D/C) model has proven to be a better alternative compared to the relatively incomplete image acquisition models commonly used in image restoration. Because it is more comprehensive, the C/D/C model offers a basis for developing significantly better restoration filters. The C/D/C model uses Fourier domain techniques to account for system blur at the image formation level, for the potentially important effects of aliasing, for additive noise and for blur at the image reconstruction level.;This dissertation develops a wavelet-based representation for the C/D/C model, including a theoretical treatment of convolution and sampling. This wavelet-based C/D/C model representation is used to formulate the image restoration problem as a generalized least squares problem. The use of wavelets discretizes the image acquisition kernel, and in this way the image restoration problem is also discrete. The generalized least squares problem is solved using the singular value decomposition. Because image restoration is only meaningful in the presence of noise, restoration solutions must deal with the issue of noise amplification. In this dissertation the treatment of noise is addressed with a restoration parameter related to the singular values of the discrete image acquisition kernel. The restoration procedure is assessed using simulated scenes and real scenes with various degrees of smoothness, in the presence of noise. All these scenes are restoration-challenging because they have a considerable amount of spatial detail at small scale. An empirical procedure that provides a good initial guess of the restoration parameter is devised

Hirschman optimal transform least mean square adaptive filters.

Abstract not available