A new lossless scalable coding based on a lossless wavelet transform (LWT) and a lossless multi-channel prediction (LMP) is proposed. A rough image can be expanded from a part of the bit stream for the use of progressive transmission. The LMP, a non-separable 2D filter bank, is optimized for an arbitrary input image signal so that remaining correlation of the band signals of the LWT can be utilized. Filter coefficients are optimized for each of input images under the lossless coding gain.

In this report, we propose an integrated lossy and lossless image coding, which is possible to be implemented on one architecture, based on combination of lossless wavelet transform (LWT) and lossy-lossless multi-channel prediction (LLMP). The LWT is applied to divide input signals into frequency subbands as octave-band decomposition, whereas the LLMP is designed as a non-separable two-dimensional filter bank including quantization step size and local decoding to enhance coding performance in both lossless coding and lossy coding. Its filter coefficients are determined to minimize total bit rate for lossless coding, and the optimum quantization step size is applied to maximize lossy coding gain. The local decoding is applied to avoid quantization error effect. The experimental results confirm effectiveness of our proposed method.

In this paper, we propose a bit-rate adaptive coding system based on lossless DCT (L-DCT). Our adaptive coding system consists of three different operation modes: lossless, near-lossless and lossy coding modes. Quantization is applied in transform domain (after the L-DCT) and spatial domain (before the L-DCT) in lossy mode and near-lossless mode, respectively. Our adaptive coding system can automatically select its operation mode at a given bit rate because it contains a function to calculate the turning point between near-lossless mode and lossy mode from characteristic of input signal. Existence of the turning point is mathematically proved in this paper. Simulation results confirm not only effectiveness of our adaptive coding system but also accuracy of our theoretical analysis.

In this paper, we propose lossless/lossy coding criterion as a new objective criterion to theoretically evaluate coding performance of the lossless/lossy wavelet (LLW). The proposed lossless/lossy coding criterion consists of three parameters: "lossless coding criterion," "quantization-lossy coding gain" and "rounding errors. " The first parameter is a criterion to evaluate lossless coding performance of the LLW, whereas the second and the third parameters are criteria to evaluate lossy coding performance of the LLW at low bit rate and high bit rate, respectively. Relation among those three parameters is clearly illustrated in this paper. Performances of 15 kinds of the LLW are measured with two-dimensional (2D) octave-decomposition by applying some standard images and 2D AR(1) model as input signals.

In this paper, we propose a new one-dimensional (1D) integer discrete cosine transform (Int-DCT) for unified lossless/lossy image compression. The proposed 1D Int-DCT is newly designed to reduce rounding effects by minimizing number of rounding operations. The proposed Int-DCT can be operated not only lossless coding for a high quality decoded image but also lossy coding for a compatibility with the conventional DCT-based coding system. Both theoretical analysis and simulation results confirm an effectiveness of the proposed Int-DCT.

An unwrapping of signal coefficients in transform domain is proposed for applications in which a lossy operation is performed on the coefficients between analysis and synthesis. It is shown that the unwrapping-based modification of signal-to-additive-signal ratio can employ the fact that an implementation of a biorthogonal decomposition is characterized by a mutually orthogonal eigenvectors. An example to illustrate the benefits of the presented approach in lossy image compression applications is shown.

The lifting wavelet transform (WT) has been widely applied to image coding. Recently, the total number of lifting steps has been minimized introducing a non-separable 2D structure so that delay from input to output can be reduced in parallel processing. However the minimum lifting WT has a problem that its upper bound of the rate-distortion curve is lower than that of the standard lifting WT. This is due to the rounding noise generated inside the transform in its integer implementation. This paper reduces the rounding noise introducing channel scaling. The channel scaling is designed so that the dynamic range of signal values is fully utilized at each channel inside the transform. As a result, the signal to noise ratio is increased and therefore the upper bound of the minimum lifting WT in lossy coding is improved.