Wavelet packet image coding using space-frequency quantization

Space-frequency quantization for image compression with directionlets

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.

Directionlets: anisotropic multidirectional representation with separable filtering

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based perfect reconstruction and critically sampled anisotropic M-DIR WT. The transform retains the separable filtering and subsampling and the simplicity of computations and filter design from the standard two-dimensional WT, unlike in the case of some other directional transform constructions (e.g., curvelets, contourlets, or edgelets). The corresponding anisotropic basis unctions (directionlets) have directional vanishing moments along any two directions with rational slopes. Furthermore, we show that this novel transform provides an efficient tool for nonlinear approximation of images, achieving the approximation power O(N(-1.55)), which, while slower than the optimal rate O(N(-2)), is much better than O(N(-1)) achieved with wavelets, but at similar complexity.

Space-frequency quantiser design for ultrasound image compression based on minimum description length criterion

The paper addresses the problem of how the spatial quantisation mode and subband adaptive uniform scalar quantiser can be jointly optimised in the minimum description length (MDL) framework for compression of ultrasound images. It has been shown that the statistics of wavelet coefficients in the medical ultrasound (US) image can be better approximated by the generalised Student t-distribution. By combining these statistics with the operational rate-distortion (RD) criterion, a space-frequency quantiser (SFQ) called the MDL-SFQ was designed, which used an efficient zero-tree quantisation technique for zeroing out the tree-structured sets of wavelet coefficients and an adaptive scalar quantiser to quantise the non-zero coefficients. The algorithm used the statistical 'variance of quantisation error' to achieve the different bit-rates ranging from near-lossless to lossy compression. Experimental results showed that the proposed coder outperformed the set partitioning in hierarchical trees (SPIHT) image coder both quantitatively and qualitatively. It yielded an improved compression performance of 1.01 dB over the best zero-tree based coder SPIHIT at 0.25 bits per pixel when averaged over five ultrasound images.

Wavelet coding of volumetric medical datasets

Several techniques based on the three-dimensional (3-D) discrete cosine transform (DCT) have been proposed for volumetric data coding. These techniques fail to provide lossless coding coupled with quality and resolution scalability, which is a significant drawback for medical applications. This paper gives an overview of several state-of-the-art 3-D wavelet coders that do meet these requirements and proposes new compression methods exploiting the quadtree and block-based coding concepts, layered zero-coding principles, and context-based arithmetic coding. Additionally, a new 3-D DCT-based coding scheme is designed and used for benchmarking. The proposed wavelet-based coding algorithms produce embedded data streams that can be decoded up to the lossless level and support the desired set of functionality constraints. Moreover, objective and subjective quality evaluation on various medical volumetric datasets shows that the proposed algorithms provide competitive lossy and lossless compression results when compared with the state-of-the-art.

Adaptive wavelet packet basis selection for zerotree image coding

Image coding methods based on adaptive wavelet transforms and those employing zerotree quantization have been shown to be successful. We present a general zerotree structure for an arbitrary wavelet packet geometry in an image coding framework. A fast basis selection algorithm is developed; it uses a Markov chain based cost estimate of encoding the image using this structure. As a result, our adaptive wavelet zerotree image coder has a relatively low computational complexity, performs comparably to state-of-the-art image coders, and is capable of progressively encoding images.

New image compression techniques using multiwavelets and multiwavelet packets

Advances in wavelet transforms and quantization methods have produced algorithms capable of surpassing the existing image compression standards like the Joint Photographic Experts Group (JPEG) algorithm. For best performance in image compression, wavelet transforms require filters that combine a number of desirable properties, such as orthogonality and symmetry. However, the design possibilities for wavelets are limited because they cannot simultaneously possess all of the desirable properties. The relatively new field of multiwavelets shows promise in obviating some of the limitations of wavelets. Multiwavelets offer more design options and are able to combine several desirable transform features. The few previously published results of multiwavelet-based image compression have mostly fallen short of the performance enjoyed by the current wavelet algorithms. This paper presents new multiwavelet transform and quantization methods and introduces multiwavelet packets. Extensive experimental results demonstrate that our techniques exhibit performance equal to, or in several cases superior to, the current wavelet filters.

Fast adaptive wavelet packet image compression

Wavelets are ill-suited to represent oscillatory patterns: rapid variations of intensity can only be described by the small scale wavelet coefficients, which are often quantized to zero, even at high bit rates. Our goal is to provide a fast numerical implementation of the best wavelet packet algorithm in order to demonstrate that an advantage can be gained by constructing a basis adapted to a target image. Emphasis is placed on developing algorithms that are computationally efficient. We developed a new fast two-dimensional (2-D) convolution decimation algorithm with factorized nonseparable 2-D filters. The algorithm is four times faster than a standard convolution-decimation. An extensive evaluation of the algorithm was performed on a large class of textured images. Because of its ability to reproduce textures so well, the wavelet packet coder significantly out performs one of the best wavelet coder on images such as Barbara and fingerprints, both visually and in term of PSNR.

A progressive transmission image coder using linear phase uniform filterbanks as block transforms

This paper presents a novel image coding scheme using M-channel linear phase perfect reconstruction filterbanks (LPPRFBs) in the embedded zerotree wavelet (EZW) framework introduced by Shapiro (1993). The innovation here is to replace the EZWs dyadic wavelet transform by M-channel uniform-band maximally decimated LPPRFBs, which offer finer frequency spectrum partitioning and higher energy compaction. The transform stage can now be implemented as a block transform which supports parallel processing and facilitates region-of-interest coding/decoding. For hardware implementation, the transform boasts efficient lattice structures, which employ a minimal number of delay elements and are robust under the quantization of lattice coefficients. The resulting compression algorithm also retains all the attractive properties of the EZW coder and its variations such as progressive image transmission, embedded quantization, exact bit rate control, and idempotency. Despite its simplicity, our new coder outperforms some of the best image coders published previously in the literature, for almost all test images (especially natural, hard-to-code ones) at almost all bit rates.