Multispectral image compression using the wavelet transform

Multispectral images contain information from several spectral wavelengths and currently multispectral images are widely used in remote sensing and they are becoming more common in the field of computer vision and in industrial applications. Typically, one multispectral image in remote sensing may occupy hundreds of megabytes of disk space and several this kind of images may be received from a single measurement. This study considers the compression of multispectral images. The lossy compression is based on the wavelet transform and we compare the suitability of different waveletfilters for the compression. A method for selecting a wavelet filter for the compression and reconstruction of multispectral images is developed. The performance of the multidimensional wavelet transform based compression is compared to other compression methods like PCA, ICA, SPIHT, and DCT/JPEG. The quality of the compression and reconstruction is measured by quantitative measures like signal-to-noise ratio. In addition, we have developed a qualitative measure, which combines the information from the spatial and spectral dimensions of a multispectral image and which also accounts for the visual quality of the bands from the multispectral images.

A Technique for Digital Color Image Watermarking Using ICA

With the increase of use of digital media the need for the methods of multimedia protection becomes extremely important. The number of the solutions to the problem from encryption to watermarking is large and is growing every year. In this work digital image watermarking is considered, specifically a novel method of digital watermarking of color and spectral images. An overview of existing methods watermarking of color and grayscale images is given in the paper. Methods using independent component analysis (ICA) for detection and the ones using discrete wavelet transform (DWT) and discrete cosine transform (DCT) are considered in more detail. A novel method of watermarking proposed in this paper allows embedding of a color or spectral watermark image into color or spectral image consequently and successful extraction of the watermark out of the resultant watermarked image. A number of experiments have been performed on the quality of extraction depending on the parameters of the embedding procedure. Another set of experiments included the test of the robustness of the algorithm proposed. Three techniques have been chosen for that purpose: median filter, low-pass filter (LPF) and discrete cosine transform (DCT), which are a part of a widely known StirMark - Image Watermarking Robustness Test. The study shows that the proposed watermarking technique is fragile, i.e. watermark is altered by simple image processing operations. Moreover, we have found that the contents of the image to be watermarked do not affect the quality of the extraction. Mixing coefficients, that determine the amount of the key and watermark image in the result, should not exceed 1% of the original. The algorithm proposed has proven to be successful in the task of watermark embedding and extraction.

Wavelet Filter Parameterization for Compression of Spectral Images

Vaatimus kuvatiedon tiivistämisestä on tullut entistä ilmeisemmäksi viimeisen kymmenen vuoden aikana kuvatietoon perustuvien sovellutusten myötä. Nykyisin kiinnitetään erityistä huomiota spektrikuviin, joiden tallettaminen ja siirto vaativat runsaasti levytilaa ja kaistaa. Aallokemuunnos on osoittautunut hyväksi ratkaisuksi häviöllisessä tiedontiivistämisessä. Sen toteutus alikaistakoodauksessa perustuu aallokesuodattimiin ja ongelmana on sopivan aallokesuodattimen valinta erilaisille tiivistettäville kuville. Tässä työssä esitetään katsaus tiivistysmenetelmiin, jotka perustuvat aallokemuunnokseen. Ortogonaalisten suodattimien määritys parametrisoimalla on työn painopisteenä. Työssä todetaan myös kahden erilaisen lähestymistavan samanlaisuus algebrallisten yhtälöiden avulla. Kokeellinen osa sisältää joukon testejä, joilla perustellaan parametrisoinnin tarvetta. Erilaisille kuville tarvitaan erilaisia suodattimia sekä erilaiset tiivistyskertoimet saavutetaan eri suodattimilla. Lopuksi toteutetaan spektrikuvien tiivistys aallokemuunnoksen avulla.

Wavelet Analysis in Turbulence

The objective of this thesis is to study wavelets and their role in turbulence applications. Under scrutiny in the thesis is the intermittency in turbulence models. Wavelets are used as a mathematical tool to study the intermittent activities that turbulence models produce. The first section generally introduces wavelets and wavelet transforms as a mathematical tool. Moreover, the basic properties of turbulence are discussed and classical methods for modeling turbulent flows are explained. Wavelets are implemented to model the turbulence as well as to analyze turbulent signals. The model studied here is the GOY (Gledzer 1973, Ohkitani & Yamada 1989) shell model of turbulence, which is a popular model for explaining intermittency based on the cascade of kinetic energy. The goal is to introduce better quantification method for intermittency obtained in a shell model. Wavelets are localized in both space (time) and scale, therefore, they are suitable candidates for the study of singular bursts, that interrupt the calm periods of an energy flow through various scales. The study concerns two questions, namely the frequency of the occurrence as well as the intensity of the singular bursts at various Reynolds numbers. The results gave an insight that singularities become more local as Reynolds number increases. The singularities become more local also when the shell number is increased at certain Reynolds number. The study revealed that the singular bursts are more frequent at Re ~ 107 than other cases with lower Re. The intermittency of bursts for the cases with Re ~ 106 and Re ~ 105 was similar, but for the case with Re ~ 104 bursts occured after long waiting time in a different fashion so that it could not be scaled with higher Re.

Wavelets in real-time paper web analysis

Online paper web analysis relies on traversing scanners that criss-cross on top of a rapidly moving paper web. The sensors embedded in the scanners measure many important quality variables of paper, such as basis weight, caliper and porosity. Most of these quantities are varying a lot and the measurements are noisy at many different scales. The zigzagging nature of scanning makes it difficult to separate machine direction (MD) and cross direction (CD) variability from one another. For improving the 2D resolution of the quality variables above, the paper quality control team at the Department of Mathematics and Physics at LUT has implemented efficient Kalman filtering based methods that currently use 2D Fourier series. Fourier series are global and therefore resolve local spatial detail on the paper web rather poorly. The target of the current thesis is to study alternative wavelet based representations as candidates to replace the Fourier basis for a higher resolution spatial reconstruction of these quality variables. The accuracy of wavelet compressed 2D web fields will be compared with corresponding truncated Fourier series based fields.

Methods for the analysis of two dimensional measurement data of paper web

This work is devoted to the problem of reconstructing the basis weight structure at paper web with black{box techniques. The data that is analyzed comes from a real paper machine and is collected by an o®-line scanner. The principal mathematical tool used in this work is Autoregressive Moving Average (ARMA) modelling. When coupled with the Discrete Fourier Transform (DFT), it gives a very flexible and interesting tool for analyzing properties of the paper web. Both ARMA and DFT are independently used to represent the given signal in a simplified version of our algorithm, but the final goal is to combine the two together. Ljung-Box Q-statistic lack-of-fit test combined with the Root Mean Squared Error coefficient gives a tool to separate significant signals from noise.

Lossless compression of hyperspectral images

Technological progress has made a huge amount of data available at increasing spatial and spectral resolutions. Therefore, the compression of hyperspectral data is an area of active research. In somefields, the original quality of a hyperspectral image cannot be compromised andin these cases, lossless compression is mandatory. The main goal of this thesisis to provide improved methods for the lossless compression of hyperspectral images. Both prediction- and transform-based methods are studied. Two kinds of prediction based methods are being studied. In the first method the spectra of a hyperspectral image are first clustered and and an optimized linear predictor is calculated for each cluster. In the second prediction method linear prediction coefficients are not fixed but are recalculated for each pixel. A parallel implementation of the above-mentioned linear prediction method is also presented. Also,two transform-based methods are being presented. Vector Quantization (VQ) was used together with a new coding of the residual image. In addition we have developed a new back end for a compression method utilizing Principal Component Analysis (PCA) and Integer Wavelet Transform (IWT). The performance of the compressionmethods are compared to that of other compression methods. The results show that the proposed linear prediction methods outperform the previous methods. In addition, a novel fast exact nearest-neighbor search method is developed. The search method is used to speed up the Linde-Buzo-Gray (LBG) clustering method.

Prediction in transformed images

The study is related to lossless compression of greyscale images. The goal of the study was to combine two techniques of lossless image compression, i.e. Integer Wavelet Transform and Differential Pulse Code Modulation to attain better compression ratio. This is an experimental study, where we implemented Integer Wavelet Transform, Differential Pulse Code Modulation and an optimized predictor model using Genetic Algorithm. This study gives encouraging results for greyscale images. We achieved a better compression ration in term of entropy for experiments involving quadrant of transformed image and using optimized predictor coefficients from Genetic Algorithm. In an other set of experiments involving whole image, results are encouraging and opens up many areas for further research work like implementing Integer Wavelet Transform on multiple levels and finding optimized predictor at local levels.

Analysis of outliers in electricity spot prices with exampleof New England and New Zealand markets

Electricity spot prices have always been a demanding data set for time series analysis, mostly because of the non-storability of electricity. This feature, making electric power unlike the other commodities, causes outstanding price spikes. Moreover, the last several years in financial world seem to show that ’spiky’ behaviour of time series is no longer an exception, but rather a regular phenomenon. The purpose of this paper is to seek patterns and relations within electricity price outliers and verify how they affect the overall statistics of the data. For the study techniques like classical Box-Jenkins approach, series DFT smoothing and GARCH models are used. The results obtained for two geographically different price series show that patterns in outliers’ occurrence are not straightforward. Additionally, there seems to be no rule that would predict the appearance of a spike from volatility, while the reverse effect is quite prominent. It is concluded that spikes cannot be predicted based only on the price series; probably some geographical and meteorological variables need to be included in modeling.

Selecting Wavelet Filter for Compression of Spectra from Multispectral Images

The problem of selecting anappropriate wavelet filter is always present in signal compression based on thewavelet transform. In this report, we propose a method to select a wavelet filter from a predefined set of filters for the compression of spectra from a multispectral image. The wavelet filter selection is based on the Learning Vector Quantization (LVQ). In the training phase for the test images, the best wavelet filter for each spectrum has been found by a careful compression-decompression evaluation. Certain spectral features are used in characterizing the pixel spectra. The LVQ is used to form the best wavelet filter class for different types of spectra from multispectral images. When a new image is to be compressed, a set of spectra from that image is selected, the spectra are classified by the trained LVQand the filter associated to the largest class is selected for the compression of every spectrum from the multispectral image. The results show, that almost inevery case our method finds the most suitable wavelet filter from the pre-defined set for the compression.

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.

Experimental and discrete element simulation studies of bell-less charging of blast furnace

This thesis presents an experimental study and numerical study, based on the discrete element method (DEM), of bell-less charging in the blast furnace. The numerical models are based on the microscopic interaction between the particles in the blast furnace charging process. The emphasis is put on model validation, investigating several phenomena in the charging process, and on finding factors that influence the results. The study considers and simulates size segregation in the hopper discharging process, particle flow and behavior on the chute, which is the key equipment in the charging system, using mono-size spherical particles, multi-size spheres and nonspherical particles. The behavior of the particles at the burden surface and pellet percolation into a coke layer is also studied. Small-scale experiments are used to validate the DEM models.

Stability Analysis in Multicriteria Discrete Portfolio Optimization.

Almost every problem of design, planning and management in the technical and organizational systems has several conflicting goals or interests. Nowadays, multicriteria decision models represent a rapidly developing area of operation research. While solving practical optimization problems, it is necessary to take into account various kinds of uncertainty due to lack of data, inadequacy of mathematical models to real-time processes, calculation errors, etc. In practice, this uncertainty usually leads to undesirable outcomes where the solutions are very sensitive to any changes in the input parameters. An example is the investment managing. Stability analysis of multicriteria discrete optimization problems investigates how the found solutions behave in response to changes in the initial data (input parameters). This thesis is devoted to the stability analysis in the problem of selecting investment project portfolios, which are optimized by considering different types of risk and efficiency of the investment projects. The stability analysis is carried out in two approaches: qualitative and quantitative. The qualitative approach describes the behavior of solutions in conditions with small perturbations in the initial data. The stability of solutions is defined in terms of existence a neighborhood in the initial data space. Any perturbed problem from this neighborhood has stability with respect to the set of efficient solutions of the initial problem. The other approach in the stability analysis studies quantitative measures such as stability radius. This approach gives information about the limits of perturbations in the input parameters, which do not lead to changes in the set of efficient solutions. In present thesis several results were obtained including attainable bounds for the stability radii of Pareto optimal and lexicographically optimal portfolios of the investment problem with Savage's, Wald's criteria and criteria of extreme optimism. In addition, special classes of the problem when the stability radii are expressed by the formulae were indicated. Investigations were completed using different combinations of Chebyshev's, Manhattan and Hölder's metrics, which allowed monitoring input parameters perturbations differently.