Browsing by Author "Orchard, Michael T."
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Item Exploring Spatial Resolution in Image Processing(2021-04-30) Yu, Lantao; Orchard, Michael T.; Baraniuk, Richard G.; Pitkow, Xaq; Kyrillidis, Anastasios; Guleryuz, Onur G.Motivated by the human visual system’s instinct to explore details, image processing algorithms designed to facilitate the viewer’s interpretation of details in an image are ubiquitous. Such algorithms seek to extract the highest spatial frequency information that an original image has to offer, and to render that information clearly to the viewer in the form of an image with often an increased number of pixels. This thesis focuses on methods for extracting the highest possible spatial frequency information from digital imagery. Classical sampling theory provides a full understanding of the highest possible spatial frequency information that can be represented by sampled images that have been spatially band-limited to the Nyquist rate. However, natural digital images are rarely band-limited and often carry substantial energy (and information) at frequencies well beyond the Nyquist rate. My research investigates approaches for extracting information from this out-of-band (beyond the Nyquist frequency limit) energy and proposes algorithms to use that information to generate images with higher spatial resolution. This thesis pursues three approaches to extracting high spatial frequency information from digital imagery, based on frequency, spatial, and cross-channel perspectives to the problem. a) Coefficients representing out-of-band high-frequency contents are closely related to co-located coefficients representing in-band, low-frequency contents. The frequency perspective seeks to exploit those relationships to estimate both the uncorrupted out-of-band and in-band coefficients representing an image with higher spatial resolution; b) Spatial patches (blocks of pixels) of an image are known to be similar to other spatial patches elsewhere in the image. Thus, a patch with high-resolution details that has an insufficient number of samples to accurately represent its details could benefit from its similarity to other spatial patches. Although each individual patch may still be insufficiently sampled to retain its details, the ensemble of samples from the collection of similar patches provides a richer sampling pattern that I seek to exploit in the spatial perspective to the problem; c) In some imaging settings, multiple electro-magnetic channels of images are available from the same scene, with different imaging modalities offering different sensor information, each with its own spatial resolution. The cross-channel perspective seeks to exploit cross-channel proximity to produce high-resolution versions of multiple channels.Item Location-oriented sampling(2007) Singh, Prashant; Orchard, Michael T.In this work we present a sampling scheme that uses feature-location information to compactly represent the data. Traditional Nyquist sampling leverages compact frequency support to form the representation, but it ignores location when doing so. Instead, our location-oriented method (LOM) uses coarse location estimates to allow a reduced-rate representation of fine-scale data. We apply a model of local symmetry to the fine-scale data, motivated by features in natural signals. We present an analysis of the concepts behind LOM as well as performance results on synthetic and natural signals.Item Noncoherent image denoising(2005) Hua, Gang; Orchard, Michael T.The techniques of Translation Invariant (TI) denoising and statistical modeling are widely used in image denoising. This thesis studies how these techniques exploit location information in images and identifies a class of noncoherent image denoising algorithms. We analyze the performance of TI denoising from the perspective of cyclic-basis reconstruction. It shows that TI denoising achieves an average performance without direct estimation of location information. Motivated by this perspective, we propose a Redundant Quaternion Wavelet Transform (RQWT) which both avoids aliasing and separates local signal energy and location information into quaternion magnitude and phases respectively. RQWT is a natural framework for studying the statistical models in noncoherent image denoisers, because they all ignore quaternion phases. Straightforward signal estimation in the RQWT framework closely matches the state-of-the-art noncoherent image denoisers and provides a natural bound on their performance, thereby showing the importance of exploring location information in quaternion phases.Item Power optimization in multiple transmit antenna communication systems(2004) Nallapureddy, Bhaskar Venkat-Vamsee; Orchard, Michael T.We explore optimal ways of communicating (with a power constraint) over multiple antenna communication systems by managing spatial power distribution. We find that Mutual Coupling (MC), the interaction between antenna elements of an array, determines the power efficient schemes. MC at the transmit array affects the amount of power drawn from the supply, and this power can be calculated by integrating the power radiated by the array in all directions. In this thesis, we focus on two problems, both of them assuming knowledge of perfect channel state information: (a) Finding the Signal to Noise Ratio maximizing scheme for Multiple Input Single Output channels, and (b) Determining the capacity achieving scheme for Multiple Input Multiple Output channels. Our solutions, Coupling Optimized BeamForming and Coupling Optimized WaterFilling outperform beamforming and waterfilling respectively, and the extent to which they do better depends on the strength of MC.Item Spatial and Temporal Image Prediction with Magnitude and Phase Representations(2011) Hua, Gang; Orchard, Michael T.In this dissertation, I develop the theory and techniques for spatial and temporal image prediction with the magnitude and phase representation of the Complex Wavelet Transform (CWT) or the over-complete DCT to solve the problems of image inpainting and motion compensated inter-picture prediction. First, I develop the theory and algorithms of image reconstruction from the analytic magnitude or phase of the CWT. I prove the conditions under which a signal is uniquely specified by its analytic magnitude or phase, propose iterative algorithms for the reconstruction of a signal from its analytic CWT magnitude or phase, and analyze the convergence of the proposed algorithms. Image reconstruction from the magnitude and pseudo-phase of the over-complete DCT is also discussed and demonstrated. Second, I propose simple geometrical models of the CWT magnitude and phase to describe edges and structured textures and develop a spatial image prediction (inpainting) algorithm based on those models and the iterative image reconstruction mentioned above. Piecewise smooth signals, structured textures and their mixtures can be predicted successfully with the proposed algorithm. Simulation results show that the proposed algorithm achieves appealing visual quality with low computational complexity. Finally, I propose a novel temporal (inter-picture) image predictor for hybrid video coding. The proposed predictor enables successful predictive coding during fades, blended scenes, temporally decorrelated noise, and many other temporal evolutions that are beyond the capability of the traditional motion compensated prediction methods. The proposed predictor estimates the transform magnitude and phase of the desired motion compensated prediction by exploiting the temporal and spatial correlations of the transform coefficients. For the case of implementation in standard hybrid video coders, the over-complete DCT is chosen over the CWT. Better coding performance is achieved with the state-of-the-art H.264/AVC video encoder equipped with the proposed predictor. The proposed predictor is also successfully applied to image registration.