Sharif Digital Repository

Compressed Sensing (CS) technique refers to the digitalization process that efficiently reduces the number of measurements below the Nyquist rate while preserving signal structure. This technique was originally developed for the analysis of vector datasets. An x ∈R^n vector is transformed into an y ∈R^m vector so that n≪m. For a sufficient number of measurements, this transformation has been shown to preserve the signal structure. Therefore, the technique has been applied to machine learning applications.2D-CS was further developed for matrices (image datasets) so that they could be directly applied to matrices without flattening. X ∈R^(n×n) is transformed into Y ∈R^(m×m) via 2D-CD such... 

By generalizing dictionary learning (DL) algorithms to Multidimensional (MD) mode and using them in applications where signals are inherently multidimensional, such as in three-dimensional (3D) Inverse Synthetic Aperture Radar (ISAR) imaging, it is possible to achieve much higher speed and less computational complexity. In this thesis, the formulation of the Multidimensional Dictionary Learning (MDDL) problem is expressed and six algorithms are proposed to solve it. The first one is based on the method of optimum directions (MOD) algorithm for 1D dictionary learning (1DDL), which uses alternating minimization and gradient projection approach. As the MDDL problem is non-convex, the second... 

Magnetic resonance imaging (MRI) is a highly efficient method that can provide acceptable contrast between soft tissues. But the big disadvantage of this method is that its acquisition is slow. To find the reason of being time-consuming should the procedure be surveyed. In the magnetic resonance imaging, location information obtained using phase and frequency encoding gradients. So the output is matrix of image data in the frequency domain, which is called k space. For the formation of the k space phase, need to apply gradients several times and this is the main reason of dullness of the system. Therefore, in this project using software methods try to reduce the scan time as possible. Among... 

Due to multiple transmit-receive channels, the signal model in a MIMO radar system is usually described by high dimensional data structures. However, the desired target space (e.g. range-azimuth domain) which shall be estimated, is mainly sparse (the number of existing targets is usually small). This observation has promoted the use of sparse recovery methods in multi-target detection and estimation in such radar systems which led to introducing the concept of compressive sensing (CS) based MIMO radars. Successful implementation of CS techniques for recovery of radar scenes (for target detection/estimation) from the received noisy measurements strongly entails that the associated sensing... 

Although up to now different processing algorithms have been proposed for Synthetic Aperture Radar (SAR) raw data, all of them suffer from one common problem and that is huge amount of data to be processed. So because of current system limitations, efficient compression algorithms for processing, saving, or transmitting data are needed. Up to now many algorithms have been proposed for SAR raw data compression, but each of them has some defects that should be payed attention to. The most important reason of these defects is the special characteristics of SAR images. With the aid of “Compressed Sensing (CS)”, the new field which has emerged recently, a special characteristic of the scene... 

The remote sensing is the knowledge of gaining information about an event without having direct access to it, and synthetic aperture radars (SAR) have gained spectacular attention in this filed due to their wide applications and high efficiency. The performance of SAR, which are classified in the space-borne or space-borne radars is similar to that of pulse radars. The transmitted signals in SAR are generally chirp signals, and the received signal is two-dimensional which is scattered in two dimensions of range and azimuth called as raw data. Due to relative movement between the radar base and the target point, the distance between the radar base and the target point would not be fixed along... 

Recently, millimeter wave imaging (MMWI) technology is given more attention. This is as a result of three facts. First, despite the infrared or optical cameras, these systems can image a target, which is obscured by one or more optically barriers. Second, the electronics circuits in this band have seen great achievements in the current decade, which facilitate the implementation of MMWI structures. Third, there is no known health hazard for the systems operating in this band with moderate power. Therefore, in this project, a MMWI system based on compressed sensing (CS) for the concealed weapon detection application is proposed. This design consists of a linear antenna array, an appropriate... 

The main motivation behind compressive sensing is to reduce the sampling rate at the input of a discrete-time signal processing system. However, if for processing the sensed signal one requires to reconstruct the corresponding Nyquist samples, then the data rate will be again high in the processing stages of the overall system. Therefore, it is preferred that the desired processing task is done directly on the compressive measurements, without the need for the reconstruction of the Nyquist samples. This thesis addresses the cases in which the processing task is “detection and/or estimation”. Firstly, a detector/estimator is proposed for compressed sensing radars, which does not need to... 

Monitoring of soil moisture plays an essential role in correct decision making and implementation of any closed loop control system in precision agriculture. On the one hand, continuous using of a lot of moisture sensors and monitoring of soil moisture via direct measurement is restricted by practical prohibitions. On the grounds that activation of a lot of sensors continuously requires communication of a large amount of information and causes high power consumption for a moisture monitoring system. On the other hand, using remote sensing methods such as satellite methods, for moisture monitoring in arbitrary spatial and time resolution for control purposes, is not practically possible. The... 

Compressive Sensing (CS) is a new paradigm in signal processing and information theory, which proposes to sample and compress sparse signals simultaneously and has drawn much attention in recent years. Many signals in lots of applications have a sparse representation in some bases, so CS is used as an efficient way of data compression in many applications such as image processing and medical applications in the last couple of years. Since some of the distributed information in complex networks are compressible too, CS can be used in order to gather the distribted information on the nodes or links efficiently. Traffic analysis and performance monitoring in computer networks, topology... 

The emerging field of compressed sensing deals with the techniques of combining the two blocks of sampling and compression into a single unit without compromising the performance. Clearly, this is not feasible for any general signal; however, if we restrict the signal to be sparse, it becomes possible. There are two main challenges in compressed sensing, namely the sampling process and the reconstruction methods. In this thesis, we will focus only on the deterministic sampling process as opposed to the random sampling. The sampling methods discussed in the literature are mainly linear, i.e., a matrix is used as the sampling operator. Here, we first consider linear sampling methods and... 

Analog-to-digital conversion and signal processing has been increasing due to its many advantages. So that mostly we prefer to convert signal from analog area to digital samples, then they are processed and finaly put the result signal at the system output. How ever because the restriction of the sampling rate, Prevent the spread of digital processing for the high-frequency signal (RF). In recent years, ADCs sampling rate rise up to several GHz (for example ADC with 4 GSPS and 12 bits for TI) that output of the these ADCs by powerful and fast FPGAs are processed but According to Shannon theorem band width of these ADCs is not desirable.the goal of this thesis uses of the compressed sensing... 

Sparse representation and compressed sensing have been widely used in various fields, one of the most popular of which is ISAR imaging. Inverse Synthetic Aperture Radar (ISAR) provides an electromagnetic image of the target, which is mainly used to identify and classify targets. In some applications, recognizing targets from a 2D image can be difficult and error-prone. One idea to deal with this problem is 3D ISAR imaging. The most widely used method of ISAR imaging is direct method based on Fourier transform. This method requires the measurement of radar data with high measurement density in 3 directions, which increases the data collection time and volume, which is the main problem of... 

Recovery of low-rank matrices from compressed linear measurements is an extension for the more well-known topic of recovery of sprse vectors from underdetermined measurements.Since the natural approach (i.e., rank minimization) for recovery of low-rank matrices is generally NP-hard, several alternatives have been proposed. However, there is a large gap between what can be achieved from these alternatives and the natural approach in terms of maximum rank of the unique solutions and the error of recovery. To narrow this gap, two novel algorithms are proposed. The main idea of both algorithms is to closely approximate the rank with a smooth function of singular values and then minimize the... 

Sparse signal processing (SSP), as a powerful tool and an efficient alternative to traditional complete transforms, has become a focus of attention during the last decade. In this ap-proach, we want to approximate a given signal as a linear combination of as few as possible basis signals. Each basis signal is called an atom and their collection is called a dictionary. This problem is generally difficult and belongs to the NP-hard problems; since it requires a combinatorial search. In recent years however, it has been shown both theoretically and experimentally that the sparset possible representation of a signal in an overcomplete dictio-nary is unique under some conditions and can be found in... 

Orthogonal Frequency Division Multiplexing (OFDM) is a digital transmission method developed to meet the increasing demand for higher data rates in communications which can be used in both wired and wireless environments. This thesis describes the issue of the Peak to Average Power Ratio (PAPR) in OFDM system, based on compressed sensing at the receiver of a peak-reducing sparse clipper applied to an OFDM signal at the transmitter. By choosing proper clipping threshold, clipping signal will be sparse so locations, magnitudes, and phases of the clipping signal can be recovered by compressed sensing method. We demonstrate that in the absence of optimization algorithms at the transmitter,... 

In recent years, the Cognitive Radio Network has received significant attentions due to its high potential for better employment of the spectrum. One of the most important parts of this technology is the spectrum sensing that requires being fast and accurate. The conventional algorithms proposed so far encounter some fundamental challenges at low SNR regimes and in wideband sensing. On the other hand, the compressed sensing algorithms, which take advantages of the sparsity of the signal of interest and utilize measurements instead of the samples, can reduce the sampling rate and thus decrease the complexity associated with the wideband sensing. In this thesis, by exploiting the... 

The design of deterministic sensing matrices is an important issue in compressive sensing in sparse signal processing. Various designs using finite field structures, combinatorics, and coding theory have been presented. The contribution of this thesis is designing many codes with large minimum distance using algebraic curves. Here, we initially design a algebraic-geometric code over a maximal curve in a Galoi field Fpm Afterwards, we map the code to the field Fp using trace map. This code has a large minimum distance. Using this code, we design a matrix with low coherence. One of the main issues in presented designs is that the number of matrix rows is considered to specific integers near... 

Sampling and recovery of a signal is one of the crucial issues in communication systems. In conventional methods, proper recovery is achieved by sampling the signal at the Nyquist rate, which is twice the signal bandwidth. There have been attempts on reducing the required sampling rate, all of which end in rates equal to a factor of the signal bandwidth. Assuming the sparse nature of the signal in hand, which is a reasonable assumption in many real world scenarios, the theory of Compressed Sensing suggests a sampling rate much less than the Nyquist rate. Designing suitable sensing matrices and efficient recovery of the signal from its samples are the two major challenges of Compressed... 

Channel estimation is one of the fundamental challenges in every communication system and different algorithms have been proposed to deal with it. Obviously, type of a communication channel is an important factor in choosing the appropriate method for channel estimation. Sparse channels are one kind of them that occur in many real-world applications such as wireless communication systems. In addition, emergence of a new means in signal processing to deal with sparse signals, known as Compressed Sensing(CS), paved the way for their extensive usage in many applications including sparse channel estimation.On the other hand, one of the most fundamental problems in sparse signal recovery using CS...