Application of Bandelet Transform in Image and Video Compression

The need for large-scale storage and transmission of data is growing exponentially With the widespread use of computers so that efficient ways of storing data have become important. With the advancement of technology, the world has found itself amid a vast amount of information. An efficient method has to be generated to deal with such amount of information. Data compression is a technique which minimizes the size of a file keeping the quality same as previous. So more amount of data can be stored in memory space with the help of data compression. There are various image compression standards such as JPEG, which uses discrete cosine transform technique and JPEG 2000 which uses discrete wavelet transform technique. The discrete cosine transform gives excellent compaction for highly correlated information. The computational complexity is very less as it has better information packing ability. However, it produces blocking artifacts, graininess, and blurring in the output which is overcome by the discrete wavelet transform. The image size is reduced by discarding values less than a prespecified quantity without losing much information. But it also has some limitations when the complexity of the image increases. Wavelets are optimal for point singularity however for line singularities and curve singularities these are not optimal. They do not consider the image geometry which is a vital source of redundancy. Here we analyze a new type of bases known as bandelets which can be constructed from the wavelet basis which takes an important source of regularity that is the geometrical redundancy.The image is decomposed along the direction of geometry. It is better as compared to other methods because the geometry is described by a flow vector rather than edges. it indicates the direction in which the intensity of image shows a smooth variation. It gives better compression measure compared to wavelet bases. A fast subband coding is used for the image decomposition in a bandelet basis. It has been extended for video compression. The bandelet transform based image and video compression method compared with the corresponding wavelet scheme. Different performance measure parameters such as peak signal to noise ratio, compression ratio (PSNR), bits per pixel (bpp) and entropy are evaluated for both Image and video compression

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

A Hierarchical Bayesian Model for Frame Representation

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyper-parameters is derived. Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyper-parameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyper-parameters. Application to practical problems of image denoising show the impact of the resulting Bayesian estimation on the recovered signal quality

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