Image data compression based on a multiresolution signal model

Image data compression is an important topic within the general field of image processing. It has practical applications varying from medical imagery to video telephones, and provides significant implications for image modelling theory. In this thesis a new class of linear signal models, linear interpolative multiresolution models, is presented and applied to the data compression of a range of natural images. The key property of these models is that whilst they are non- causal in the two spatial dimensions they are causal in a third dimension, the scale dimension. This leads to computationally efficient predictors which form the basis of the data compression algorithms. Models of varying complexity are presented, ranging from a simple stationary form to one which models visually important features such as lines and edges in terms of scale and orientation. In addition to theoretical results such as related rate distortion functions, the results of applying the compression algorithms to a variety of images are presented. These results compare favourably, particularly at high compression ratios, with many of the techniques described in the literature, both in terms of mean squared quantisation noise and more meaningfully, in terms of perceived visual quality. In particular the use of local orientation over various scales within the consistent spatial interpolative framework of the model significantly reduces perceptually important distortions such as the blocking artefacts often seen with high compression coders. A new algorithm for fast computation of the orientation information required by the adaptive coder is presented which results in an overall computational complexity for the coder which is broadly comparable to that of the simpler non-adaptive coder. This thesis is concluded with a discussion of some of the important issues raised by the work

Wavelet Analysis and Denoising: New Tools for Economists

This paper surveys the techniques of wavelets analysis and the associated methods of denoising. The Discrete Wavelet Transform and its undecimated version, the Maximum Overlapping Discrete Wavelet Transform, are described. The methods of wavelets analysis can be used to show how the frequency content of the data varies with time. This allows us to pinpoint in time such events as major structural breaks. The sparse nature of the wavelets representation also facilitates the process of noise reduction by nonlinear wavelet shrinkage , which can be used to reveal the underlying trends in economic data. An application of these techniques to the UK real GDP (1873-2001) is described. The purpose of the analysis is to reveal the true structure of the data - including its local irregularities and abrupt changes - and the results are surprising.Wavelets, Denoising, Structural breaks, Trend estimation

Video Coding with Motion-Compensated Lifted Wavelet Transforms

This article explores the efficiency of motion-compensated three-dimensional transform coding, a compression scheme that employs a motion-compensated transform for a group of pictures. We investigate this coding scheme experimentally and theoretically. The practical coding scheme employs in temporal direction a wavelet decomposition with motion-compensated lifting steps. Further, we compare the experimental results to that of a predictive video codec with single-hypothesis motion compensation and comparable computational complexity. The experiments show that the 5/3 wavelet kernel outperforms both the Haar kernel and, in many cases, the reference scheme utilizing single-hypothesis motion-compensated predictive coding. The theoretical investigation models this motion-compensated subband coding scheme for a group of K pictures with a signal model for K motion-compensated pictures that are decorrelated by a linear transform. We utilize the Karhunen-Loeve Transform to obtain theoretical performance bounds at high bit-rates and compare to both optimum intra-frame coding of individual motion-compensated pictures and single-hypothesis motion-compensated predictive coding. The investigation shows that motion-compensated three-dimensional transform coding can outperform predictive coding with single-hypothesis motion compensation by up to 0.5 bits/sample

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Coupling 2D-wavelet decomposition and multivariate image analysis (2D WT-MIA)

[EN] The use of 2D discrete wavelet transform in the feature enhancement phase of multivariate image analysis is discussed and implemented in a comparative way with respect to previous publications. In the proposed approach, all the resulting subimages obtained by discrete wavelet transform decomposition are unfolded pixel-wise and midlevel data fused to a feature matrix that is used for the feature analysis phase. Congruent subimages can be obtained either by reconstruction of each decomposition block to the original pixel dimensions or by using the stationary wavelet transform decomposition scheme. The main advantage is that all possible relationships among blocks, decomposition levels, and channels are assessed in a single multivariate analysis step (feature analysis). This is particularly useful in a monitoring context where the aim is to build multivariate control charts based on images. Moreover, the approach can be versatile for contexts where several images are analyzed at a time as well as in the multispectral image analysis. Both a set of simple artificial images and a set of real images, representative of the on-line quality monitoring context, will be used to highlight the details of the methodology and show how the wavelet transform allows extracting features that are informative of how strong the texture of the image is and in which direction it varies. 2D Wavelet Transform (DWT or SWT) in the Feature Enhancement phase of Multivariate Image Analysis is compared to current state of art. Wavelet-decomposition images are unfolded pixel-wise and mid-level datafused to a Feature Matrix so that all relationships among blocks, decomposition levels and channels are assessed in a single multivariate Feature Analysis step. The approach is suitable in process monitoring context. Also, denoising and background removal are obtained at WT decomposition stage, and it can be easily extended to hyperspectral images.Li Vigni, M.; Prats-Montalbán, JM.; Ferrer, A.; Cocchi, M. (2018). Coupling 2D-wavelet decomposition and multivariate image analysis (2D WT-MIA). Journal of Chemometrics. 32(1):1-20. https://doi.org/10.1002/cem.2970S12032

Super Resolution of Wavelet-Encoded Images and Videos

In this dissertation, we address the multiframe super resolution reconstruction problem for wavelet-encoded images and videos. The goal of multiframe super resolution is to obtain one or more high resolution images by fusing a sequence of degraded or aliased low resolution images of the same scene. Since the low resolution images may be unaligned, a registration step is required before super resolution reconstruction. Therefore, we first explore in-band (i.e. in the wavelet-domain) image registration; then, investigate super resolution. Our motivation for analyzing the image registration and super resolution problems in the wavelet domain is the growing trend in wavelet-encoded imaging, and wavelet-encoding for image/video compression. Due to drawbacks of widely used discrete cosine transform in image and video compression, a considerable amount of literature is devoted to wavelet-based methods. However, since wavelets are shift-variant, existing methods cannot utilize wavelet subbands efficiently. In order to overcome this drawback, we establish and explore the direct relationship between the subbands under a translational shift, for image registration and super resolution. We then employ our devised in-band methodology, in a motion compensated video compression framework, to demonstrate the effective usage of wavelet subbands. Super resolution can also be used as a post-processing step in video compression in order to decrease the size of the video files to be compressed, with downsampling added as a pre-processing step. Therefore, we present a video compression scheme that utilizes super resolution to reconstruct the high frequency information lost during downsampling. In addition, super resolution is a crucial post-processing step for satellite imagery, due to the fact that it is hard to update imaging devices after a satellite is launched. Thus, we also demonstrate the usage of our devised methods in enhancing resolution of pansharpened multispectral images