Joint space-frequency segmentation using balanced wavelet packet trees for least-cost image representation

On the number of rectangular tilings

Adaptive multiscale representations via quadtree splitting and two-dimensional (2-D) wavelet packets, which amount to space and frequency decompositions, respectively, are powerful concepts that have been widely used in applications. These schemes are direct extensions of their one-dimensional counterparts, in particular, by coupling of the two dimensions and restricting to only one possible further partition of each block into four subblocks. In this paper, we consider more flexible schemes that exploit more variations of multidimensional data structure. In the meantime, we restrict to tree-based decompositions that are amenable to fast algorithms and have low indexing cost. Examples of these decomposition schemes are anisotropic wavelet packets, dyadic rectangular tilings, separate dimension decompositions, and general rectangular tilings. We compute the numbers of possible decompositions for each of these schemes. We also give bounds for some of these numbers. These results show that the new rectangular tiling schemes lead to much larger sets of 2-D space and frequency decompositions than the commonly-used quadtree-based schemes, therefore bearing the potential to obtain better representation for a given image.

Fast search for best representations in multitree dictionaries

We address the best basis problem--or, more generally, the best representation problem: Given a signal, a dictionary of representations, and an additive cost function, the aim is to select the representation from the dictionary which minimizes the cost for the given signal. We develop a new framework of multitree dictionaries, which includes some previously proposed dictionaries as special cases. We show how to efficiently find the best representation in a multitree dictionary using a recursive tree-pruning algorithm. We illustrate our framework through several examples, including a novel block image coder, which significantly outperforms both the standard JPEG and quadtree-based methods and is comparable to embedded coders such as JPEG2000 and SPIHT.

Wavelet-based space-frequency compression of ultrasound images

This paper describes the compression of grayscale medical ultrasound images using a recent compression technique, i.e., space-frequency segmentation (SFS). This method finds the rate-distortion optimal representation of an image from a large set of possible space-frequency partitions and quantizer combinations and is especially effective when the images to code are statistically inhomogeneous, which is the case for medical ultrasound images. We implemented a compression application based on this method and tested the algorithm on representative ultrasound images. The result is an effective technique that performs better than a leading wavelet-transform coding algorithm, i.e., set partitioning in hierarchical trees (SPIHT), using standard objective distortion measures. To determine the subjective qualitative performance, an expert viewer study was run by presenting ultrasound radiologists with images compressed using both SFS and SPIHT. The results confirmed the objective performance rankings. Finally, the performance sensitivity of the space-frequency codec is shown with respect to several parameters, and the characteristic space-frequency partitions found for ultrasound images are discussed.

Lagrange wavelets for signal processing

This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach combines the perceptually dependent visual group normalization (VGN) technique and a softer logic masking (SLM) method. These are utilized to rescale the wavelet coefficients, remove perceptual redundancy and obtain good visual performance for digital image processing.

Wavelet packet image coding using space-frequency quantization

We extend our previous work on space-frequency quantization (SFQ) for image coding from wavelet transforms to the more general wavelet packet transforms. The resulting wavelet packet coder offers a universal transform coding framework within the constraints of filterbank structures by allowing joint transform and quantizer design without assuming a priori statistics of the input image. In other words, the new coder adaptively chooses the representation to suit the image and the quantization to suit the representation. Experimental results show that, for some image classes, our new coder gives excellent coding performance.