Solomon A Tesfamicael

This paper provides clustered compressive sensing (CCS) based signal processing using Bayesian framework. Images like magnetic resonanse images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. Compressed sensing (CS) paradigm can be applied in order to boost such signal recoveries. We applied CS paradigm via Bayesian framework. That is incorporating the different prior information such as sparsity and the special structure that can be found in such sparse signal improves signal recovery. The method is applied on synthetic and medical images including MRI images. The results show that applying the clustered compressive sensing out performs the non clustered but only sparse counter parts when it comes to mean square error(MSE), pick signal to noise ratio (PSNR) and other performance metrics.

Existing initiatives in mathematics education demand establishing a continuous professional development program for teachers in Ethiopian schools. However, implementing such programs first requires an understanding of the school and district environment in which the participating teachers work, as mathematics instruction is in part a function of the environment. In many cases, school and district settings are dynamic, and it is difficult to incorporate unplanned and intervening factors into the change process. This case study attempts to investigate the influences of the school and district settings in promoting reform visions in mathematics education. This study applies the theory of communities of practice as a framework and qualitative coding of data to understand the dynamic school setting and its implications for the teaching practices of mathematics teachers. The findings reveal that the school setting does not adequately promote reform visions, but rather it maintains the pra...

ABSTRACT The sum capacity of a broadcast MIMO channel can be achieved sub-optimally using linear precoding techniques. Block diagonalization (BD) is a linear precoding technique that achieves near to the sum capacity with low complexity by nullifying the inter-user interference. However, one limitation of BD is that the equivalent channel after block diagonalization has to be communicated to the users using additional pilot symbols or a limited feedforward link. The former method increases the system overhead and the latter suffers from quantization error. Transmitter zero forcing may be an alternative but it has a high power enhancement. Besides, transmitter zero forcing lacks flexibility for use in multi-antenna users. In this paper, a new linear precoding technique called Block Diagonalization Inversion (BDI) is proposed. The proposed scheme avoids the need to communicate the equivalent channel by using a combination of block diagonalization and partial inversion of the equivalent channel at the transmitter. BDI enables per-stream power alloca- tion and adaptive modulation like BD; besides, BDI has a lower power enhancement than transmitter zero forcing. It is shown using simulations that BDI achieves a sum rate performance in-between an ideal BD and transmitter zero forcing. When a limited feedforward link is used with BD, it is demonstrated that BDI provides higher sum rate than BD.

This paper provides a compressive sensing (CS) method of denoising images using Bayesian framework. Some images, for example like magnetic resonance images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. So denoising boosts the true signal strength. Under Bayesian framework, we have used two different priors: sparsity and clusterdness in an image data as prior information to remove noise. Therefore, it is named as clustered compressive sensing based denoising (CCSD). After developing the Bayesian framework, we applied our method on synthetic data, Shepp-logan phantom and sequences of fMRI images. The results show that applying the CCSD give better results than using only the conventional compressive sensing (CS) methods in terms of Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). In addition, we showed that this algorithm could have some advantages over the state-of-the-art methods like Block-Matching and 3D Fil...

This chapter provides the use of Bayesian inference in compressive sensing (CS), a method in signal processing. Among the recovery methods used in CS literature, the convex relaxation methods are reformulated again using the Bayesian framework and this method is applied in different CS applications such as magnetic resonance imaging (MRI), remote sensing, and wireless communication systems, specifically on multipleinput multiple-output (MIMO) systems. The robustness of Bayesian method in incorporating prior information like sparse and structure among the sparse entries is shown in this chapter.

This chapter provides the use of Bayesian inference in compressive sensing (CS), a method in signal processing. Among the recovery methods used in CS literature, the convex relaxation methods are reformulated again using the Bayesian framework and this method is applied in different CS applications such as magnetic resonance imaging (MRI), remote sensing, and wireless communication systems, specifically on multipleinput multiple-output (MIMO) systems. The robustness of Bayesian method in incorporating prior information like sparse and structure among the sparse entries is shown in this chapter.

This thesis deals with an emerging area of signal processing, called Compressive Sensing (CS), that allows the reconstruction of sparse or compressible signals from fewer measurements than are used in traditional schemes. Like traditional signal representation schemes, CS follows a similar framework: encoding, transmission/storing, and decoding. The encoding part is done using random projection (RP) or random sensing, and the decoding is done via nonlinear reconstruction algorithms from a reduced amount of measurements. The performance of the reconstruction schemes used and the application of such paradigm are the two main focuses of the thesis. It has three parts: the introduction, performance analysis of recovery algorithms in CS and some applications of CS. The introductory part provides the background for the following four chapters. It begins by defining the basic concepts used in CS theory and presents the Bayesian framework. Further, an analytical tool from statistical mechan...

Channel adaptive transmission requires knowledge of channel state information at the transmitter. In temporally correlated MIMO channels, the correlation can be utilized to reduce feedback overhead and improve performance. In this paper, Compressed Sensing (CS) methods and rotative quantization are used to compress and feedback channel state information for MIMO systems as an extension work of [1]. Using simulation, it is shown that the CS based method reduces feedback overhead while delivering the same performance as the direct quantization scheme.

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from statistical mechanics, especially called replica method. This method has been used to analyze communication systems like Code Division Multiple Access (CDMA) and multiple input multi- ple output (MIMO) systems with large size. Replica analysis, now days rigorously proved, is an efficient tool to analyze large systems in general. Specifically, we analyze the performance of some of the estimators used in CS like LASSO (the Least Absolute Shrinkage and Selection Operator) estimator and Zero-Norm regularizing estimator as a special case of maximum a posteriori (MAP) estimator by using Bayesian framework to connect the CS estimators and replica method. We use both replica symmetric (RS) ansatz and one-step replica symmetry breaking (1RSB) ansatz, clamm...

A new method of compressive sensing reconstruction is presented. The method assumes that the signal to be estimated is both sparse and clustered. These properties are modeled as a modified Laplacian prior in a Bayesian setting, resulting in two penalizing terms in the corresponding unconstrained minimization problem. In the implementation an equivalent constrained minimization problem is solved using quadratic programming. Experiments on images with noisy observations show a significant gain when including the clustered assumption compared to the traditional LASSO approach only penalizing for sparsity. Further more, the algorithm performs better than the algorithms like CluSS-MCMC, CluSS-VB for the types of signals we have considered in this research.