Wavelet Based Image Coding Schemes : A Recent Survey <s> SFQ (Space -Frequency Quantization) <s> A new class of image coding algorithms coupling standard scalar quantization of frequency coefficients with tree-structured quantization (related to spatial structures) has attracted wide attention because its good performance appears to confirm the promised efficiencies of hierarchical representation. This paper addresses the problem of how spatial quantization modes and standard scalar quantization can be applied in a jointly optimal fashion in an image coder. We consider zerotree quantization (zeroing out tree-structured sets of wavelet coefficients) and the simplest form of scalar quantization (a single common uniform scalar quantizer applied to all nonzeroed coefficients), and we formalize the problem of optimizing their joint application. We develop an image coding algorithm for solving the resulting optimization problem. Despite the basic form of the two quantizers considered, the resulting algorithm demonstrates coding performance that is competitive, often outperforming the very best coding algorithms in the literature. <s> BIB001 </s> Wavelet Based Image Coding Schemes : A Recent Survey <s> SFQ (Space -Frequency Quantization) <s> The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, to provide a good visual quality of compressed images, it is fundamental to preserve good reconstruction of these directional features. In our previous work, we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments imposed in the corresponding basis functions along different directions, called directionlets. In this paper, we show how to design and implement a novel efficient space-frequency quantization (SFQ) compression algorithm using directionlets. Our new compression method outperforms the standard SFQ in a rate-distortion sense, both in terms of mean-square error and visual quality, especially in the low-rate compression regime. We also show that our compression method, does not increase the order of computational complexity as compared to the standard SFQ algorithm. <s> BIB002
The standard separable 2-D wavelet transform has lately achieved great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and make many large magnitude wavelet coefficients. Since contours are very important elements in the visual perception of images, it is fundamental to preserve good reconstruction of these directional features to provide a good visual quality of compressed images. This is achieved by spacefrequency quantization (SFQ) compression algorithm using directionlets BIB002 . SFQ BIB001 is a wavelet based image coding scheme that fits itself into a new class of image coding algorithms which combines standard scalar quantization of frequency coefficients with the tree structured quantization. The performance of the algorithm is very good and appears to confirm the promised efficiencies of hierarchical representation. The Space -Frequency Quantization technique exploits both spatial and frequency compaction property of the wavelet transforms through the use of two simple quantization modes. It defines a symbol that indicates a spatial region of high frequency coefficients having zero value. This is to exploit the spatial compaction property. Application of this symbol is told as zero-tree quantization, because it involves setting to zero a tree-structured set of wavelet coefficients. This is done in the first phase which is called Tree Pruning Algorithm. In the next phase, called Predicting the Tree, the relation between a spatial region in image and the tree -structured set of coefficients is exploited. A mechanism for pointing to the location where high frequency coefficients are clustered is called Zero tree quantization. Thus, this quantization mode directly exploits the spatial clustering of high frequency coefficients predicted. For coefficients that are not set to zero by the zero tree quantization, a common uniform scalar quantization, independent of coefficient frequency band, is applied. Nearly optimal coding efficiency is provided by uniform scalar quantization followed by entropy coding.