Sparse Signal Expansion Theories And Their Applications To Image Enhancement

As well known, wavelet analysis can be used to describe the signal with point singularities effectively. However, for the signals with singularities distributed along various curves, curve surface and hyper-curve-surface in high dimensional space, Wavelet analysis loses its advantages. Under this situation, sparse signal expansion theories, a kind of new multiscale analysis theory that has been developed in recent years, possess a better performance in detecting the singularities of the signal with straight line or curve in high dimensional space and can be used to express signals with sparse coefficients. So sparse signal expansion theories have been widely used in the field of image processing, including image compression,image enhancement and image denoising and etc. This paper first introduces two basic algorithms of spare signal expansion, ridgelet transform and curvelet transform, and gives their implementation. Then the applications of ridgelet transform and curvelet transform in image processing are discussed. Being one of the important branches of image processing, image enhancement is used as a target application for spare signal expansion. And two kinds of images are served as testbed to illustrate the detailed applications of the ridgelet and curvelet transforms. First, for the problem of detecting the dim and small targets in the infrared image, a curvelet-based background suppression algorithm is proposed for enhancing the infrared targets. Secondly, for the problem of the fingerprint image enhancement, a novel enhancement algorithm based on radon and ridgelet transforms is presented with good performance. The experimental results demonstrate the effectiveness of the spare signal expansion in the applications of image enhancement. Finally, Theories and applications of some other sparse signal expansion methods are also givens.