Compressed Sensing Performance Analysis via Replica Method using Bayesian framework

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, clamming the latter is efficient when the problem is not convex. This work is more analytical in its form. It is deferred for next step to focus on the numerical results.Comment: The analytical work and results were presented at the 2012 IEEE European School of Information Theory in Antalya, Turkey between the 16th and the 20th of Apri

Bayesian Inference and Compressed Sensing

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 multiple-input 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

Synchronization in Digital Receivers

Estimating the frequency of received signals is an attractive topic in communicationtheory. In this work, some of these estimators are introduced. Also, a generalization oftwo of these estimators are derived. Performance of the estimators are compared togetherfor several preamble lengths, signal-to-noise values and steps. Generalized estimatorsattain the Cramer-Rao lower bound for lower signal-to-noise ratio values if the rightstep value is used. The computation complexity of the estimators is calculated anddiscussed. Also it is shown that computation complexity depends on how an algorithmis implemented by calculating computation complexity for two separate implementationsof a single estimator

Clustered Compressive Sensing: Application on Medical Imaging

his paper provides clustered compressive sensing (CCS) based image processing using Bayesian framework applied to medical images. 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. Compressed sensing (CS) paradigm can be applied in order to boost such signals. We applied CS paradigm via Bayesian framework. Using different sparse prior information and in addition incorporating the special structure that can be found in sparse signal, CCS can be applied to improve image processing. This is shown in the results of this paper. First, we applied our analysis on Angiogram image, then on Shepp-logan phantom and finally on another MRI image. The results show that applying the clustered compressive sensing give better results than the non-clustered version

Estimation of Missing Data in Fetal Heart Rate Signals Using Shift-Invariant Dictionary

In 2015, an estimated 1.3 million intrapartum stillbirths occurred, meaning that the fetus died during labour. The majority of these stillbirths occurred in low and middle income countries. With the introduction of affordable continuous fetal heart rate (FHR) monitors for use in these settings, the fetal well-being can be better monitored and health care personnel can potentially intervene at an earlier time if abnormalities in the FHR signal are detected. Additional information about the fetal health can be extracted from the fetal heart rate signals through signal processing and analysis. A challenge is, however, the large number of missing samples in the recorded FHR as fetal and maternal movement in addition to sensor displacement can cause data dropouts. Previously proposed methods perform well on estimation of short dropouts, but struggle with data from wearable devices with longer dropouts. Sparse representation and dictionary learning have been shown to be useful in the related problem of image inpainting. The recently proposed dictionary learning algorithm, SI-FSDL, learns shift-invariant dictionaries with long atoms, which could be beneficial for such time series signals with large dropout gaps. In this paper it is shown that using sparse representation with dictionaries learned by SI-FSDL on the FHR signals with missing samples provides a reconstruction with improved properties compared to previously used techniques