Integer fast lapped transforms based on direct-lifting of DCTs for lossy-to-lossless image coding

Abstract

The discrete cosine transforms (DCTs) have found wide applications in image/video compression (image coding). DCT-based lapped transforms (LTs), called fast LTs (FLTs), overcome blocking artifacts generated at low bit rate image coding by DCT while keeping fast implementation. This paper presents a realization of more effective integer FLT (IntFLT) for lossy-to-lossless image coding, which is unified lossless and lossy image coding, than the conventional IntFLTs. It is composed of few operations and direct application of DCTs to lifting blocks, called direct-lifting of DCTs. Since the direct-lifting can reuse any existing software/hardware for DCTs, the proposed IntFLTs have a great potential for fast implementation which is dependent on the architecture design and DCT algorithms. Furthermore, the proposed IntFLTs do not need any side information unlike integer DCT (IntDCT) based on direct-lifting as our previous work. Moreover, they can be easily extended to larger size which is recently required as in DCT for the standard H.26x series. As a result, the proposed method shows better lossy-to-lossless image coding than the conventional IntFLTs.

A novel high-frequency encoding algorithm for image compression

“…Each block in the frequency domain consists of the following: DC-component at the first location of each block which is a measure of the average value of the samples in the block, and other coefficients called AC coefficients as described in Eq. (1) [2,6,19]:…”

“…The DCT has been extensively used [1,2] in image compression. The image is divided into segments and each segment is then subjected to the transform, creating a series of frequency components that correspond with detail levels of the image.…”

Novel methods of image compression for 3D reconstruction

“…The following equations represent theDCT and its inverse [130,131,138] The quantization table is a matrix of the same block size that can be represented as follows:…”

“…Each block in the frequency domain consist of: a DC-component at the first location of each block which is the average value of the samples in the block, and other coefficients called the AC coefficients as described in Eq. (3.1) [130,131,138].…”

“…As mentioned in previous Chapters, the Discrete Cosine Transform (DCT) is the basis of the popular JPEG file format, and most video compression methods and multi-media applications are generally based on it [117,119,127,138]. In other words, the image is divided into segments and the DCT is then applied to each segment creating a series of frequency components that correspond with detail levels of the image.…”