An Image Filter Based on Multiobjective Genetic Algorithm and Shearlet Transformation

Rician noise pollutes magnetic resonance imaging (MRI) data, making data’s postprocessing difficult. In order to remove this noise and avoid loss of details as much as possible, we proposed a filter algorithm using both multiobjective genetic algorithm (MOGA) and Shearlet transformation. Firstly, the multiscale wavelet decomposition is applied to the target image. Secondly, the MOGA target function is constructed by evaluation methods, such as signal-to-noise ratio (SNR) and mean square error (MSE). Thirdly, MOGA is used with optimal coefficients of Shearlet wavelet threshold value in a different scale and a different orientation. Finally, the noise-free image could be obtained through inverse wavelet transform. At the end of the paper, experimental results show that this proposed algorithm eliminates Rician noise more effectively and yields better peak signal-to-noise ratio (PSNR) gains compared with other traditional filters

Randomized Signal Processing with Continuous Frames

This paper focuses on signal processing tasks in which the signal is transformed from the signal space to a higher dimensional phase space using a continuous frame, processed in this space, and synthesized to an output signal. For example, in a phase vocoder method, an audio signal is transformed to the time-frequency plane via the short time Fourier transform, manipulated there, and synthesized to an output audio signal. We show how to approximate such methods, termed phase space signal processing methods, using a Monte Carlo method. The Monte Carlo method speeds up computations, since the number of samples required for a certain accuracy is proportional to the dimension of the signal space, and not to the dimension of phase space, which is typically higher. We utilize this property for a new phase vocoder method, based on an enhanced time-frequency space, with more dimensions than the classical method. The higher dimension of phase space improves the quality of the method, while retaining the computational complexity of a standard phase vocoder based on regular samples

Directional edge and texture representations for image processing

An efficient representation for natural images is of fundamental importance in image processing and analysis. The commonly used separable transforms such as wavelets axe not best suited for images due to their inability to exploit directional regularities such as edges and oriented textural patterns; while most of the recently proposed directional schemes cannot represent these two types of features in a unified transform. This thesis focuses on the development of directional representations for images which can capture both edges and textures in a multiresolution manner. The thesis first considers the problem of extracting linear features with the multiresolution Fourier transform (MFT). Based on a previous MFT-based linear feature model, the work extends the extraction method into the situation when the image is corrupted by noise. The problem is tackled by the combination of a "Signal+Noise" frequency model, a refinement stage and a robust classification scheme. As a result, the MFT is able to perform linear feature analysis on noisy images on which previous methods failed. A new set of transforms called the multiscale polar cosine transforms (MPCT) are also proposed in order to represent textures. The MPCT can be regarded as real-valued MFT with similar basis functions of oriented sinusoids. It is shown that the transform can represent textural patches more efficiently than the conventional Fourier basis. With a directional best cosine basis, the MPCT packet (MPCPT) is shown to be an efficient representation for edges and textures, despite its high computational burden. The problem of representing edges and textures in a fixed transform with less complexity is then considered. This is achieved by applying a Gaussian frequency filter, which matches the disperson of the magnitude spectrum, on the local MFT coefficients. This is particularly effective in denoising natural images, due to its ability to preserve both types of feature. Further improvements can be made by employing the information given by the linear feature extraction process in the filter's configuration. The denoising results compare favourably against other state-of-the-art directional representations

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity