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This dissertation, Binary Image Restoration by Positive Semidefinite Programming and Signomial Programming by 沈逸江, Yijiang, Shen, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Digital images are representations of scenes in the real world that contain imperfections due to degradations such as blur, noise and rounding error. One special case is when the true scenery is binary, (e.g. in documents, bar codes, handwriting signatures and vehicle license plates) but is then degraded by an additive noise, such as Gaussian white noise or salt-and-pepper noise. The goal of image restoration is to reconstruct the original scene from the degraded obser- vation. Most traditional denoising and linear deconvolution methods do not take advantage of the constraint that pixel values are binary when restoring degraded binary images. The growing interest in and development of convex programming techniques provide other alternatives for the restoration of degraded binary images. This the- sis describes work that applies the Positive Semidenite Programming method to restore binary images degraded by blur and noise. We alos use the Signomial Programming method to restore noisy binary images far faster than the Posi- tive Semidenite Programming method. Numerical experiments show that the Positive Semidenite Programming method is accurate, insensitive to noise and simple without introducing new parameters, while the Signomial Programming method is fast with good accuracy and is applicable to both degraded binary and grayscale images. { An abstract of approximately 200 words DOI: 10.5353/th_b3955743 Subjects: Image processing - Digital techniquesMathematical optimizationNonlinear programming

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