Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Sarkar, Deepayan

Abstract (Summary of the Work)

Degradation of photographic images is a common phenomenon that can occur due to several reasons. Astronomical images may be degraded due to atmospheric factors or telescope optics. Photographs taken using standard digital cameras may be blurred due to lack of focus, due to motion of the subject, due to low resolution, or due to camera shake during relatively long exposures. Often one wishes to correct for the effect of such degradation and recover the original image, and this has been a long-standing research problem in digital imaging. Effective solutions depend critically on the context of the problem and the type of degradation. Depending on the type of degradation, different types of methodologies can be adopted. At a high level, image restoration can be classified as deblurring of image, image upscaling or super resolution, image denoising, etc.In context of image deblurring, we are specifically interested in motion blur in digital photography caused by camera shake. Blurring caused by camera shake is one of the most common artifacts in amateur digital photography. Long exposures are unavoidable in low light situations, and images taken without a camera stand often result in blurry and disappointing images. Recovering an unblurred image from such a motion-blurred photograph has long been a fundamental research problem. Figure 1.1 gives some real-life examples of blurred photographs; we use these images later as representative test cases.Under-resolution is another common problem in photographs captured in low end cameras. Upsampling such images to a high resolution image is an useful problem as often it is needed to display a low resolution image in a bigger screen. Camera shake during the course of an exposure essentially means that the light supposed to fall into a single pixel is instead distributed into several neighbouring pixels in a pattern determined by the motion of the camera. This pattern is commonly referred to as the point spread function (PSF) or blur kernel. If one assumes that the PSF is shift-invariant, that is, the same PSF applies to all pixels of the underlying unblurred image, then the resulting observed image can be viewed as a convolution of the true unblurred image and the PSF. For this reason, this problem is often referred to the image deconvolution problem to distinguish it from the problem of recovering from other kinds of image degradation.The broader class of image deconvolution problems are generally separated into non-blind and blind deconvolution problems.In the next few sections, we give a precise mathematical formulation of the problem we are interested in solving, introduce a set of example images and blur kernels that we use for illustration throughout the thesis, and describe the prior on underlying true images that has been successully used by Fergus et al. and Levin et al. We end this chapter with a brief outline of the discrete Fourier transform (DFT) and its properties, as it is used extensively throughout this thesis. In Chapters 2 and 3, we briefly review previous work on non-blind and blind deconvolution, respectively. Chapter 4 describes in detail the approach of Levin et al., which we use as a basis for our generalization for the blind deconvolution problem, although in principle our methods can be used to generalize any method based on a similar prior. We describe the motivation for our proposed generalization of image priors in Chapter 5, along with simple applications. We discuss non-blind deconvolution and super-resolution (upsampling) using the generalized prior in Chapter 6, and blind deconvolution in Chapter 7. Finally, Chapter 8 reviews our findings and discusses possible future avenues of work.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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