The Tschirnhaus Transform is a method to solve quartic equations. If the quartic equation has four distinct real roots, a low computation complexity algorithm is proposed and applied to the the 10-order Line Spectrum Pairs(LSP).However, during the procedures of calculation, the existence of the inverse trigonometric functions increase the computation load of the hardware implementation. We also propose some methods to solve this problem and increase the speed of the calculation. A table of comparison result with the previous proposed Complex-Free Farrari formula is also included.

The Cartesian Cubic lattice is known to be sub optimal when consideringband-limited signals but is still used as standard in three-dimensional medical magneticresonance imaging. The optimal sampling lattices are the body-centered cubic latticeand the face-centered cubic lattice. This report discusses the possible use of thesesampling lattices in MRI and presents verification of the non standard Fouriertransform method that is required for MR image creation for these sampling lattices.The results show that the Fourier transform is consistent with analytical models.

The presence of subsurface anomalies, such as cavities, faults, unknown tunnels, etc., either natural or man-made, can cause public safety hazards. The detection of these features requires the development of new methods. Seismic Rayleigh surface wave imaging is a relatively new non-destructive testing technique (NDT) which generates subsurface images without drilling boreholes into the ground, and in recent years has been widely used for soil characterization in geotechnical investigations. In the last decade, some researchers have applied the technique to near-surface imaging and showed the possibility and potential for engineering applications. This research presents the development of a technique to process seismic Rayleigh waves to detect and image subsurface anomalies. This study conducted investigations of Rayleigh wave behaviors and developed a new strategy for Rayleigh wave isolation from raw field data. The strategy applies wavelet transforms, instead of the conventional spectral analysis of surface waves (SASW) method, or popular multichannel analysis of surface waves (MASW) techniques, to pair-channel analysis of the isolated Rayleigh wave data for dispersion calculation. Finally, a simple steady inversion technique was applied to yield shear velocity as a function of both depth and distance, and shear velocity field images (SVF), for near surface section display. This research consists of development, computer programming, field tests, data processing and interpretation. Three sites in different scenarios were used for seismic investigations: old mining tunnels in medium dipping coal seams in Stellarton coalfield, mining cavities in steeply dipping gold-bearing veins in West Waverley Gold District and an anomaly in nearly horizontal strata in Liverpool. All these sites are in the province of Nova Scotia, Canada. The results from seismic surface wave technique introduced in this research can be evaluated by field observations, documents and borehole logs. The satisfactory interpretations and success of this investigation shows that this technique is suitable for engineering application for subsurface investigations.

Remote sensing imaging is a tool for collecting information about the Earth's surface such as soil, vegetation and water. Recent progress in electronics, telecommunications and sensor developments have resulted in the launch of many satellites in the past three decades. Different sensors in remote sensing systems capture a variety of images with differing characteristics. Image fusion has been used to integrate two or more images and provides output images with better accuracy. This research provides a new technique for image fusion using the contourlet transform in combination with the YCbCr color space. The output images preserve both the spectral and spatial characteristics of the input images and they are better for human and machine interpretation. This technique provides solutions to some problems (\emph{i.e.}, ghosting effect, and blocking artifacts) which the traditional image fusion techniques fail to address. The proposed technique is tested on both classical and remote sensing images. Quality metrics are used to evaluate the results of the proposed technique. The results proved significant enhancement of the quality of the output images. More fine details are successfully captured and the original chromaticity information is preserved as well. The proposed technique eliminates the blocking artifacts in the output images. Also, a new metric is presented to measure the blocking artifacts in the fused image. The results showed that increasing the number of contourlet decomposition levels does not degrade the quality of the output image. Therefore, the output images do not lose their chromaticity information when the number of contourlet decomposition levels increases. The proposed technique is tested on a variety of the remote sensing images that have large resolution ratios (\emph{i.e.}, 1:8, 1:16 and 1:32). The proposed technique is robust and suitable for many image applications. The detection of the concealed objects is an example of such applications, where the proposed technique is tested to measure its capability to fuse images with different features. The results of the Contourlet-YCbCr fusion technique are compared with the conventional fusion methods, where the proposed technique is more capable in detecting the hidden objects and preserving the original color components of the input image.

Diss. (sammanfattning) Uppsala : Univ., 2004. / Härtill 4 uppsatser.

Thesis (Ph.D.)--University of Delaware, 2007. / Principal faculty advisor: Busby N. O. Attoh-Okine, Dept. of Civil & Environmental Engineering. Includes bibliographical references.

Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Adibi, Ali; Committee Member: Chang, Gee-Kung; Committee Member: Ralph, Stephen; Committee Member: Trebino, Rick; Committee Member: Verriest, Erik I.

Thesis (doctoral)--Tübingen, 1981.

Thesis--University of Oulu, 1985. / Includes bibliographical references (p. [21]-22).

This thesis is concerned with the development of a practical digital image processing system for recording and subsequent reconstruction of the magnitude and phase of an optical wave-front arriving from a coherently illuminated object disturbance. Since the wave-fronts of concern are coherent, the magnitude and phase of such waves are generally independent functions in the sense that the knowledge of one is not sufficient to uniquely deduce the other. To uniquely reconstruct and characterize optical disturbances both the magnitude and phase are required. In general, all recording media respond only to light intensity and no difficulty is encountered in recording the intensity and therefore the magnitude, because it is the square root of the intensity.