Search results for "Set partitioning in hierarchical trees"
showing 5 items of 5 documents
The Myriad Virtues of Wavelet Trees
2009
Wavelet Trees have been introduced in [Grossi, Gupta and Vitter, SODA '03] and have been rapidly recognized as a very flexible tool for the design of compressed full-text indexes and data compressors. Although several papers have investigated the beauty and usefulness of this data structure in the full-text indexing scenario, its impact on data compression has not been fully explored. In this paper we provide a complete theoretical analysis of a wide class of compression algorithms based on Wavelet Trees. We also show how to improve their asymptotic performance by introducing a novel framework, called Generalized Wavelet Trees, that aims for the best combination of binary compressors (like,…
Efficient image compression using directionlets
2007
Directionlets are built as basis functions of critically sampled perfect-reconstruction transforms with directional vanishing moments imposed along different directions. We combine the directionlets with the space-frequency quantization (SFQ) image compression method, originally based on the standard two-dimensional wavelet transform. We show that our new compression method outperforms the standard SFQ as well as the state-of-the-art image compression methods, such as SPIHT and JPEG-2000, in terms of the quality of compressed images, especially in a low-rate compression regime. We also show that the order of computational complexity remains the same, as compared to the complexity of the sta…
Space-Frequency Quantization using Directionlets
2007
In our previous work we proposed a construction of critically sampled perfect reconstruction transforms with directional vanishing moments (DVMs) imposed in the corresponding basis functions along different directions, called directionlets. Here, we combine the directionlets with the space-frequency quantization (SFQ) image compression method, originally based on the standard two-dimensional (2-D) wavelet transform (WT). We show that our new compression method outperforms the standard SFQ as well as the state-of-the-art compression methods, like SPIHT and JPEG-2000, in terms of the quality of compressed images, especially in a low-rate compression regime. We also show that the order of comp…
Data Compression Using Wavelet and Local Cosine Transforms
2015
The chapter describes an algorithm that compresses two-dimensional data arrays, which are piece-wise smooth in one direction and have oscillating events in the other direction. Seismic, hyper-spectral and fingerprints data, for example, have such a mixed structure. The transform part of the compression process is an algorithm that combines wavelet and local cosine transform (LCT). The quantization and the entropy coding parts of the compression are taken from the SPIHT codec. To efficiently apply the SPIHT codec to a mixed coefficients array, reordering of the LCT coefficients takes place. On the data arrays, which have the mixed structure, this algorithm outperforms other algorithms that a…
A Comparative Study and an Evaluation Framework of Multi/Hyperspectral Image Compression
2009
In this paper, we investigate different approaches for multi/hyperspectral image compression. In particular, we compare the classic multi-2D compression approach and two different implementations of 3D approach (full 3D and hybrid) with regards to variations in spatial and spectral dimensions. All approaches are combined with a weighted Principal Component Analysis (PCA) decorrelation stage to optimize performance. For consistent evaluation, we propose a larger comparison framework than the conventionally used PSNR, including eight metrics divided into three families. The results show the weaknesses and strengths of each approach.