Signal recovery from partial fractional fourier domain information and pulse shape design using iterative projections

Cataloged from PDF version of article.Signal design and recovery problems come up in a wide variety of applications in signal processing. In this thesis, we first investigate the problem of pulse shape design for use in communication settings with matched filtering where the rate of communication, intersymbol interference, and bandwidth of the signal constitute conflicting themes. In order to design pulse shapes that satisfy certain criteria such as bit rate, spectral characteristics, and worst case degradation due to intersymbol interference, we benefit from the wellknown Projections Onto Convex Sets. Secondly, we investigate the problem of signal recovery from partial information in fractional Fourier domains. Fractional Fourier transform is a mathematical generalization of the ordinary Fourier transform, the latter being a special case of the first. Here, we assume that low resolution or partial information in different fractional Fourier transform domains is available in different intervals. These information intervals define convex sets and can be combined within the Projections Onto Convex Sets framework. We present generic scenarios and simulation examples in order to illustrate the use of the method.Güven, H EmreM.S

Simultaneous use of Individual and Joint Regularization Terms in Compressive Sensing: Joint Reconstruction of Multi-Channel Multi-Contrast MRI Acquisitions

Purpose: A time-efficient strategy to acquire high-quality multi-contrast images is to reconstruct undersampled data with joint regularization terms that leverage common information across contrasts. However, these terms can cause leakage of uncommon features among contrasts, compromising diagnostic utility. The goal of this study is to develop a compressive sensing method for multi-channel multi-contrast magnetic resonance imaging (MRI) that optimally utilizes shared information while preventing feature leakage. Theory: Joint regularization terms group sparsity and colour total variation are used to exploit common features across images while individual sparsity and total variation are also used to prevent leakage of distinct features across contrasts. The multi-channel multi-contrast reconstruction problem is solved via a fast algorithm based on Alternating Direction Method of Multipliers. Methods: The proposed method is compared against using only individual and only joint regularization terms in reconstruction. Comparisons were performed on single-channel simulated and multi-channel in-vivo datasets in terms of reconstruction quality and neuroradiologist reader scores. Results: The proposed method demonstrates rapid convergence and improved image quality for both simulated and in-vivo datasets. Furthermore, while reconstructions that solely use joint regularization terms are prone to leakage-of-features, the proposed method reliably avoids leakage via simultaneous use of joint and individual terms. Conclusion: The proposed compressive sensing method performs fast reconstruction of multi-channel multi-contrast MRI data with improved image quality. It offers reliability against feature leakage in joint reconstructions, thereby holding great promise for clinical use.Comment: 13 pages, 13 figures. Submitted for possible publicatio

An augmented lagrangian method for sparse SAR imaging

In this paper, we present a solution to the constrained l1-norm minimization problem for sparse SAR imaging. The technique we present relies on recent advances in the solution of optimization problems, based on Augmented Lagrangian Methods (ALMs), namely the Alternating Direction Method of Multipliers. Here, we present an application of C-SALSA (an ALM for constrained optimization problems) to SAR imaging, and introduce a new weighting scheme to improve the sparsity of the reconstructions. We then compare the performances of several techniques to understand the effectiveness of ALMs in the context of SAR imaging

An augmented Lagrangian method for image reconstruction with multiple features

We present an Augmented Lagrangian Method (ALM) for solving image reconstruction problems with a cost function consisting of multiple regularization functions with a data fidelity constraint. The presented technique is used to solve inverse problems related to image reconstruction, including compressed sensing formulations. Our contributions include an improvement for reducing the number of computations required by an existing ALM method, an approach for obtaining the proximal mapping associated with p-norm based regularizers, and lastly a particular ALM for the constrained image reconstruction problem with a hybrid cost function including a weighted sum of the p-norm and the total variation of the image. We present examples from Synthetic Aperture Radar imaging and Computed Tomography

An augmented Lagrangian method for autofocused compressed SAR imaging

We present an autofocus algorithm for Compressed SAR Imaging. The technique estimates and corrects for 1-D phase errors in the phase history domain, based on prior knowledge that the reflectivity field is sparse, as in the case of strong scatterers against a weakly-scattering background. The algorithm relies on the Sparsity Driven Autofocus (SDA) method and Augmented Lagrangian Methods (ALM), particularly Alternating Directions Method of Multipliers (ADMM). In particular, we propose an ADMM-based algorithm that we call Autofocusing Iteratively Re-Weighted Augmented Lagrangian Method (AIRWALM) to solve a constrained formulation of the sparsity driven autofocus problem with an ℓp-norm, p ≤ 1 cost function. We then compare the performance of the proposed algorithm's performance to Phase Gradient Autofocus (PGA) and SDA [2] in terms of autofocusing capability, phase error correction, and computation time

Simple Sensor Application: Determination of Electrochemical Properties of Carvedilol in CPE Based on Zinc Oxide Nanoparticles and Development of the Method for its Determination in Pharmaceutical Samples

In the study, the electrochemical characteristics of carvedilol were determined by cyclic voltammetry and square wave voltammetry on carbon paste electrode with zinc oxide nanoparticles at pH 8.0 in Britton Robinson buffer. The adsorption characteristics of the molecule on the modified electrode and the electron number accompanying the electrode reaction were calculated. In addition, a new square wave anodic adsorptive stripping voltammetry process was suggested for the determination of carvedilol drug samples. The linear concentration range and detection limit of the process were found to be 0.07 µM–2.61 µM and 0.09 µM, respectively. Recovery studies of CAR in the pharmaceutical sample were performed to check the accuracy of the developed process. With the developed process, results with high reliability, reproduceability, accuracy and precision were obtained for the determination of CAR in pharmaceutical samples

A fast augmented Lagrangian approach for compressed SAR imaging

In this paper we present an accelerated Augmented Lagrangian Method for the solution of constrained convex optimization problems in the Basis Pursuit De-Noising (BPDN) form. The technique relies on on Augmented Lagrangian Methods (ALMs), particularly the Alternating Direction Method of Multipliers (ADMM). Here, we present an application of the Constrained Split Augmented Lagrangian Shrinkage Algorithm (C-SALSA) to SAR imaging, while introducing a method to handle complex SAR imagery in the constrained Total Variation Minimization formulation. In addition, we apply acceleration schemes to C-SALSA to obtain faster convergence of the method; such as used in Fast ADMM methods proposed by Goldstein et al., in the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) proposed by Beck and Teboulle, and in NESTA proposed by Becker et al. We present examples to illustrate the effectiveness of Accelerated C-SALSA in the context of SAR imaging

An alternating direction method of multipliers for sparse SAR imaging (Seyrek SAR görüntüleme için yön değiştiren çarpanlar yaklaşımı)

In this paper, we present a solution to the constrained 1-norm minimization problem for sparse SAR imaging. The technique we present relies on recent advances in the solution of optimization problems, based on Augmented Lagrangian Methods (ALMs), in particular the Alternating Direction Method of Multipliers. Here, we present an application of C-SALSA (an ALM for constrained optimization problems) to SAR imaging. We then compare the performances of several techniques to understand the effectiveness of ALMs in the context of SAR imaging

Bilateral Superior Cervical Ganglionectomy and Melatonin Levels in Rat Subarachnoid Hemorrhage Model: Simple Precautions May Preserve Melatonin Levels

Aim: Subarachnoid hemorrhage (SAH) is a serious disease, and it is thought that melatonin may have positive effects after SAH. Bilateral resection or blockage of superior cervical ganglions has constant effects on melatonin levels. Animal models with bilateral superior cervical ganglionectomy (SCG) show the role of superior cervical ganglion on melatonin and give clues about simple precautions which may help to prevent unfavorable outcomes in SAH patients. The aim of this study is to examine how melatonin levels change in SAH and SCG models. Material and Methods: Forty-two Sprague Dawley male rats weighing 200-250 g were used in the study and randomly divided into six groups. Arterial blood samples were collected 24 hours after the procedure in all groups. Serum melatonin levels of the groups were studied. Results: A significant difference in blood melatonin levels was observed between SAH and SCG groups, and against the control group. There was no significant difference between the melatonin levels in SCG group and SAH+SCG group (p=0.983). The mean blood melatonin level of the SAH group was higher than the SCG (p<0.001), SAH+SCG (p<0.001) and control groups (p=0.001). The mean blood melatonin levels of SAH+SCG and SCG groups were lower than the mean blood melatonin levels of the other groups and also the SAH group (p<0.001). Conclusion: Bilateral SCG significantly inhibited the abrupt increase of serum melatonin levels after SAH model in rats. Future studies aiming to address melatonin’s complex outcomes should take into account that minor exogenous factors may affect serum melatonin levels

Autofocused compressive SAR imaging based on the alternating direction method of multipliers

We present an alternating direction method of multipliers (ADMM) based autofocused Synthetic Aperture Radar (SAR) imaging method in the presence of unknown 1-D phase errors in the phase history domain, with undersampled measurements. We formulate the problem as one of joint image formation and phase error estimation. We assume sparsity of strong scatterers in the image domain, and as such use sparsity priors for reconstruction. The algorithm uses l(p)-norm minimization (p <= 1) [8] with an improvement by integrating the phase error updates within the alternating direction method of multipliers (ADMM) steps to correct the unknown 1-D phase error. We present experimental results comparing our proposed algorithm with a coordinate descent based algorithm in terms of convergence speed and reconstruction quality