Sharif Digital Repository

Cardiovascular diseases are one of the major causes of mortality in humans. One way to diagnose heart diseases and abnormalities is processing of cardiac signals such as ECG.In many of these processes, inter-beat and intra-beat features of ECG signal must be extracted. These features include peak, onset and offset of ECG waves,meaningful intervals and segments that can be defined for ECG signal. ECG fiducial point (FP) extraction refers to identifying the location of the peak as well as the onset and offset of the P-wave,QRS complex and T-wave which convey clinically useful information. However, the precise segmentation of each ECG beat is a difficult task, even for experienced... 

Transformers are one of the most important equipments in transmission and distribution networks. Transformer unplanned outages have severe impacts on the continuity of power system operation. To improve the reliability of transformers and to achieve an optimum operation cost, online condition monitoring of transformers is inevitable. Information about the quality of the transformers insulation system is known as the best parameter to be monitored in a transformer. Since partial discharge signals are initiated long before the beginning of a severe damage, partial discharge monitoring and its evaluation canbe employed to warn the operator.Data mining on the partial discharge signals extracts... 

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... 

Over-complete transforms due to their maneuverability in signal representation have been under focus during the last decade. Different properties for the representation can be useful in different applications. These properties includes minimum ℓ2 representation, minimum ℓ1 representation, minimum ℓ0 representation and so on. Among these properties, minimum ℓ0 representation (also known as sparse representation) has been shown to be efficient in many applications including image denoising, data compression, blind source separation and so on, and create a new approach in signal processing area named sparse signal processing. Sparse signal processing is based on two principles, the first one is... 

In recent years, sparse representation has had a variety of applications in computer vision such as noise reduction, image reconstruction, classification and dimension reduction. In this project, we aim to provide a method of matching the keypoints obtained from the Scale Invariant feature Transform (SIFT) algorithm. In this algorithm is used descriptor instead of intensity . The proposed method, first, extracts the salient points from the images and learns a dictionary-based descriptors corresponding to the points. Then, using the dictionary, it obtains the sparse coefficients for each salient point by which, it determines the correspondence of the salient points in the two images using SVD... 

Recent advances in data recording has lead to different modalities like text, image, audio and video. Images are annotated and audio accompanies video. Because of distinct modality statistical properties, shallow methods have been unsuccessful in finding a shared representation which maintains the most information about different modalities. Recently, deep networks have been used for extracting high-level representations for multimodal data. In previous methods, for each modality, one modality-specific network was learned. Thus, high-level representations for different modalities were extracted. Since these high-level representations have less difference than raw modalities, a shared... 

Sparse decomposition has recently attracted the attention of many researchers in dierent areas of signal processing. In mathematical viewpoint, sparse decomposition is nding a sparse solution of an Underdetermined System of Linear Equations (USLE). This concept has many applications in dierent signal processing elds including blind sourse separation, optical character recognition and image processing. In this thesis, we investigate the application of sparse decomposition in image denoising. One of the image denoising methods which is related to sparse decomposition concepts is the \transfrom domain method". In this method, the noisy image is rst transformed to another domain, and then noise... 

The sparse decomposition problem or nding sparse solutions of underdetermined linear systems of equations is one of the fundamental issues in signal processing and statistics. In recent years, this issue has been of great interest to researches in various elds of signal processing and accordingly found to be greatly benecial in those elds. This thesis aims at the investigation of the applications of the sparse decomposition problem in image processing. Among dierent applications such as compression, reconstruction, separation and image denoising, this thesis mainly focuses on the last one. One of the methods of image denoising which is closely tied to the sparse decomposition, is the method... 

Nowadays, Electroencephalogram (EEG) is the most common method for brain activity measurement. Event Related Potentials (ERP) which are recorded through EEG, have many applications. Detecting ERP signals is an important task since their amplitudes are quite small compared to the background EEG. The usual way to address this problem is to repeat the process of EEG recording several times and use the average signal. Though averaging can be helpful, there is a need for more complicated filtering. Blind source separation methods are frequently used for ERP denoising. These methods don’t use prior information for extracting sources and their use is limited to 2D problems only. To address these... 

Noise contamination is inevitable in biomedical recordings. In some cases biomedical recordings are highly contaminated with artifacts which make the effective recovering process hard to achieve. Many different methods have been proposed for artifact removal from biomedical signals but introducing an effective method which can present valuable data for medical analysis, is still an ongoing process.
This dissertation focuses on inter-ictal EEG denoising approaches including ICA-based and EMD-based methods and different combination of these methods. These methods are tested on simulated epileptic recordings which are contaminated with real muscle artifact and EEG signal. The denoised... 

Predicting the location of oil and gas recourses is the first challenge in the petroleum industry. One of the most popular and acceptable ways which can guide an explorer to the position of the resources is the seismic survey. By this kind of survey, geologists can observe inside of solid matter by using the ultrasound waves. The process works by sending sound waves to the surface and measuring the length it takes to be reflected from rocks underneath, then with recording these echoes by arrays of sensors, they can obtain a seismic image which has too noise, including ghosting, multiples (multiples are the waves that has been reflected more than once between the energy source and the... 

One of problemsin an inverse problem like history matching is there is no unique solution. This means that maybe several diferent permeability maps can correctly reproduced the history of fieldt but there is no garanttee that these maps accurately predidct reservoir production behavior. One way to face and deal with this problem, except manipulation of solution and optimization algorithm (inverse modeling) is to use other data sources like seismic data, Variogram, pore volume, and fracture density or any other parameter obtained from geostatistical investigations.Multi-resolution wavelet analysis can be an appropriate tool to gather the necessary information to characterize the inverse model... 

Sparse representation and consequently, dictionary learning have been two of the great importance topics in signal processing problems for the last two decades. In sparse representation, each signal has to be represented as a linear combination of some basic signals, which are called atoms, and their collection is called a dictionary. To put it in other words, if complete dictionaries such as Fourier or Wavelet dictionaries are used for the representation of signals, the representation will be unique, but not sparse. On the other hand, if overcomplete dictionaries are used, we will confront with too many representations, and the goal of sparse representation is to find the sparsest one. ... 

In this thesis, we focus on decomposition of a matrix into low rank and sparse matrices. We propose two algorithms. The first one is based on smoothed l0-norm where the l0-norm is approximated by smoothed one. Almost all previous works are based on l1-norm where the l0-norm is approximated by the l1-norm. The second algorithm is based on adaptive thresholding; to make a matrix low rank, its singular values are thresholded and to make a matrix sparse, its entries are also thresholded. Various simulations have been performed to compare the proposed algorithms with the previous ones. The results confirm the fact that the proposed algorithms have better performance in terms of quality and speed... 

At first, we introduce composite optimization problems some review the proposed methods to solve these problems. To solve the composite optimization problems with strongly convex objective function, recently Chamboll and Pock proposed a general fast iterative shrinkage and thresholding algorithm (GFISTA). After that, Calatroni and Chambolle proposed a backtracking strategy for this algorithm. Unlike classical Armijo-type line searching, proposed backtracking rule allows for local increasing or decreasing of the descent step size along the iterations. In this thesis, we describe this algorithm with backtracking and prove its accelerated convergence rate. We also discuss some heuristic... 

Nowadays, the use of MEMS sensors, due to their small size, lightweight and low cost, has been welcomed in systems such as autonomous vehicles. Although the precision of MEMS gyroscopes has been extremely improved, in some aspects, such as stability of bias, they still suffer from some big error sources, like run-to run bias, which determines the sensor price but is not negligible even inexpensive sensors. In addition to the bias, there are a lot of noises in the gyroscope outputs, where ARW is one of the most important ones, which causes failure in real-signals and produces an error in the position and attitude of mobile systems. Due to the fact that run-to-run bias and ARW are stochastic... 

The prevalence of epilepsy in the world and the need for surgery to treat patients have made it essential to locate the site of epilepsy before surgery. One method is to apply source localization algorithms to the EEG signals of epileptic patients in the ictal and interictal periods. However, because these signals are contaminated with various noises, they are challenging to interpret and require noise cancellation. Therefore, various methods have been proposed to eliminate the noise. Among these methods, a new method recently used to remove noise from the epileptic signal is Morphological Component Analysis (MCA). This method uses the basic concepts of sparse representation of signals to... 

The goal of the research presented in this thesis is removing noise from electrocardiogram (ECG) signals. The electrocardiogram is a test that measures the electrical activity of the heart. The information obtained from an electrocardiogram can be used to diagnose different types of heart disease. It may be useful for seeing how well the patient is responding to treatment. The extraction of high resolution ECG signals from noisy measurements is among the most tempting open problems of biomedical signal processing. Extracting useful clinical information from the real (noisy) ECG requires reliable signal processing techniques. Numerous methods have been reported to denoise ECG signals based on... 

Interictal EEG signals are very critical in diagnosis of epilepsy. Analysis of interictal EEG signals is very challenging due to contamination by various undesired signals like background EEG, muscular activity, noise, etc. Thus denoising of interictal signals has been an active research field in recent years. Primary purpose of this thesis is to denoise interictal EEG signals by using different combinations of ICA-based and wavelet denoising approaches. Then a new direction is pursued by using Morphological Component Analysis (MCA) which is a method for solving source separation problems based on morphological diversity of sources. Afterward MCA is modified by considering more prior...