We present a lifting-based lapped transform (L-LT) and a reversible symmetric extension (RSE) in the boundary processing for more effective lossy-to-lossless image coding of data with various qualities from only one piece of lossless compressed data. The proposed dual-DCT-lifting-based LT (D2L-LT) parallel processes two identical LTs and consists of 1-D and 2-D DCT-liftings which allow the direct use of a DCT matrix in each lifting coefficient. Since the DCT-lifting can utilize any existing DCT software or hardware, it has great potential for elegant implementations that are dependent on the architecture and DCT algorithm used. In addition, we present an improved RSE (IRSE) that works by recalculating the boundary processing and solves the boundary problem that the DCT-lifting-based L-LT (DL-LT) has. We show that D2L-LT with IRSE mostly outperforms conventional L-LTs in lossy-to-lossless image coding.

A simple DFT-based noise variance estimator for orthogonal frequency division multiplexing access (OFDMA) systems is proposed. The conventional DFT-based estimator differentiates the channel impulse response and noise in the time domain. However, for partial frequency response, its time domain signal will leak to all taps due to the windowing effect. The noise and channel leakage power become mixed. In order to accurately derive the noise power, we propose a novel symmetric extension method to reduce the channel leakage power. This method is based on the improved signal continuity at the boundaries introduced by symmetric extension. Numerical results show that the normalized mean square error (NMSE) of our proposed method is significantly lower than that of the conventional DFT method.

This paper describes an effective technique for coding QCIF video sequences based on a JPEG2000 codec. In the proposed method, multiple frames are combined into one large picture. The larger picture enables images to be coded more efficiently. Image quality is further improved by combining the frames symmetrically. The video sequence is efficiently coded by adapting the time correlation of the video sequences to spatial correlation. We demonstrated the effectiveness of this method by encoding QCIF video sequences using JPEG2000.

In this paper, a two-dimensional (2-D) binary-valued (BV) lapped transform (LT) is proposed. The proposed LT has basis images which take only BV elements and satisfies the axial-symmetric (AS) property. In one dimension, there is no 2-point LT with the symmetric basis vectors, and the property is achieved only with the non-overlapping basis which the Hadamard transform (HT) has. Hence, in two dimension, there is no 22-point separable ASLT, and only 2-D HT can be the 22-point separable AS orthogonal transform. By taking non-separable BV basis images, this paper shows that a 22-point ASLT can be obtained. Since the proposed LT is similar to HT, it is referred to as the lapped Hadamard transform (LHT). LHT of larger size is shown to be provided with a tree structure. In addition, LHT is shown to be efficiently implemented by a lattice structure.