Two-stage near-lossless compression of image and video

Near-lossless compression has been a popular alternative to lossy or lossless compression as it achieves significantly higher compression ratios than lossless methods while providing a certain quantitative guarantee on the amount of local distortion.;In this thesis, we first propose a novel wavelet-based two-stage near-lossless coding scheme. Unlike other similar approaches that rely upon time-consuming iterative procedures, the proposed scheme minimizes the bit rate 'on-the-fly' given a maximum error bound, capitalizing on the 'critical distortion' phenomenon. Next, we propose a method of Linfinity error scalable coding. The method presented, based upon a simple set-partitioning idea, generates extra residual layers for Linfinity error scalability. We then implement a 3D medical image compression algorithm by combining the two proposed schemes. We show that the implemented coding algorithm provides a competitive lossy-to-lossless coding performance compared with some of the best results in the literature based on integer-to-integer wavelets, with several other benefits. We further proceed with exploring the possibilities and issues of scalable lossless video coding. Two wavelet-based video coding methods with subpixel-accurate MCTF are demonstrated.;Also presented are the results of our investigation into the problem of combined denoising and compression. We point out a common misconception in the literature and show the equivalence of two popular denoisers based on lossy compression, using the concept of the critical distortion of a noisy source. Also we address the problem of efficient compression of noisy sources at high bit rates. We show that the notion of the critical distortion of a denoised source plays an important role in determining the encoding rate, the use of which leads to significant bit rate savings without noticeable fidelity loss.;Finally, we propose a class of nonlinear transforms for fast retrieval of data with a specified range of pixel values from the compressed bitstream. They are derived from the well-known linear transforms such as DCT. Promising areas of application include compression of scientific data such as digital elevation map.