Wavelet Domain Image Resolution Enhancement Methods.

Resolution enhancement of pictorial data is desirable in many applications such as monitoring, surveillance, medical imaging and remote sensing when images at desirable resolution levels are not available. It is a classic signal interpolation problem and several conventional approaches such as zero-order interpolation (sample-and-hold), bilinear and spline interpolation are widely used. However, undesirable levels of smoothing across salient edges in the higher resolution images obtained using these conventional methods resulted in a search for more effective algorithms. Recently several efforts in the field have utilised wavelet-domain methodologies with the intention of overcoming some of the problems associated with conventional treatment. In this thesis, we propose three wavelet domain image resolution enhancement algorithms. The first proposed algorithm is based on the estimation of detail wavelet coefficients at high resolution scales by exploiting the wavelet coefficient correlation in a local neighbourhood sense. The unknown detail coefficients are estimated by employing linear least-squares regression parameters of which are obtained from the quad-tree decomposition of the low-resolution image. The second algorithm starts with an initial high-resolution approximation to the original image obtained by means of zero-padding in the wavelet domain. This is further processed using the cycle spinning methodology which reduces ringing. Linear regression using a minimal training set of high-resolution originals is finally employed to rectify the degraded edges. For the third algorithm we propose a directional variant of the cycle spinning methodology with an aim of reducing the over-smoothing of salient image features as well as offering a reduction in computational complexity. In particular we take into account local edge orientation information derived from a wavelet decomposition of the available low resolution image to influence key parameters of the cycle spinning algorithm. Our results show that the proposed methods are considerably superior to conventional image interpolation techniques, both in objective and subjective terms, while also comparing favourably with competing methods.