A New Approach Based on Set Partitioning in Hierarchical Tree Algorithm for Image Compression

In this paper, the authors propose a new approach to image compression based on the principle of Set Partitioning in Hierarchical Tree algorithm （SPIHT）. Our approach, the modified SPIHT （MSPIHT）, distributes entropy differently than SPIHT and also optimizes the coding. This approach can produce results that are a significant improvement on the Peak Signal-to-Noise Ratio （PSNR） and compression ratio obtained by SPIHT algorithm, without affecting the computing time. These results are also comparable with those obtained using the Embedded Zerotree Wavelet （EZW） and Joint Photographic Experts Group 2000 （JPG2） algorithms.

Formal Photograph Compression Algorithm Based on Object Segmentation

Small storage space for photographs in formal documents is increasingly necessary in today＇s needs for huge amounts of data communication and storage. Traditional compression algorithms do not sufficiently utilize the distinctness of formal photographs. That is, the object is an image of the human head, and the background is in unicolor. Therefore, the compression is of low efficiency and the image after compression is still space-consuming. This paper presents an image compression algorithm based on object segmentation for practical high-efficiency applications. To achieve high coding efficiency, shape-adaptive discrete wavelet transforms are used to transformation arbitrarily shaped objects. The areas of the human head and its background are compressed separately to reduce the coding redundancy of the background. Two methods, lossless image contour coding based on differential chain, and modified set partitioning in hierarchical trees （SPIHT） algorithm of arbitrary shape, are discussed in detail. The results of experiments show that when bit per pixel （bpp）is equal to 0.078, peak signal-to-noise ratio （PSNR） of reconstructed photograph will exceed the standard of SPIHT by nearly 4dB.

Simultaneous Speckle Reduction and SAR Image Compression Using Multiwavelet Transform

Synthetic aperture radar （SAR） images are corrupted by multiplicative speckle noise which limits the performance of the classical coder/decoder algorithm in spatial domain. The relatively new transform of multiwavelets can possess desirable features simultaneously, such as orthogonality and symmetry, while scalar wavelets cannot. In this paper we propose a compression scheme combining with speckle noise reduction within the multiwavelet framework. Compared with classical set partitioning in hierarchical trees （SPIHT） algorithm, our method achieves favorable peak signal to noise ratio （PSNR） and superior speckle noise reduction performances.

Rate-distortion weighted SPIHT algorithm for interferometer data processing

As one of the next generation imaging spectrometers, the interferential spectrometer （iS） possesses the advantages of high throughput, multi-channel and great resolution. The data of IS are produced in the spatial domain, but optical applications are in the Fourier domain. Traditional compression methods can only protect the visual quality of interferometer data in the spatial do- main but ignore the distortion in the Fourier domain. The relation between the distortion in the Fourier domain and the compression in the spatial domain is analyzed. By mathematical proof and val- idation with experiments, the relation between spatial and Fourier domains is discovered, and the significance in the Fourier domain is more important as optical path difference （OPD） increasing in the spatial domain. Based on this relation, a novel coding scheme is proposed, which can compress data in the spatial domain while reducing the distortion in the Fourier domain. In this scheme, the bit stream of the set partitioning in hierarchical trees （SPIHT） is truncated by adaptively lifting rate-distortion slopes according to the priorities of OPD based on rate-distortion optimization theory. Experimental results show that the proposed method can provide better protection of spectrum curves in the Fourier domain while maintaining a comparable visual quality in the spatial domain.

New Edge-Directed Interpolation Based-Lifting DWT and MSPIHT Algorithm for Image Compression

The amount of image data generated in multimedia applications is ever increasing. The image compression plays vital role in multimedia applications. The ultimate aim of image compression is to reduce storage space without degrading image quality. Compression is required whenever the data handled is huge they may be required to sent or transmitted and also stored. The New Edge Directed Interpolation (NEDI)-based lifting Discrete Wavelet Transfrom (DWT) scheme with modified Set Partitioning In Hierarchical Trees (MSPIHT) algorithm is proposed in this paper. The NEDI algorithm gives good visual quality image particularly at edges. The main objective of this paper is to be preserving the edges while performing image compression which is a challenging task. The NEDI with lifting DWT has achieved 99.18% energy level in the low frequency ranges which has 1.07% higher than 5/3 Wavelet decomposition and 0.94% higher than traditional DWT. To implement this NEDI with Lifting DWT along with MSPIHT algorithm which gives higher Peak Signal to Noise Ratio (PSNR) value and minimum Mean Square Error (MSE) and hence better image quality. The experimental results proved that the proposed method gives better PSNR value (39.40 dB for rate 0.9 bpp without arithmetic coding) and minimum MSE value is 7.4.

A simple and efficient method for image transmission over inferior channel

The constrained Viterbi algorithm （C-VA） makes use of some prior reliable information to reduce complexity and improve performance of Viterbi algorithm （VA）. However it can only be used in the concatenate code scheme because the detection result of cyclic redundancy check code （CRC） is exploited to provide reliable information. In this paper, a different way is proposed to provide reliable information for C-VA, which is possible to be used in simple codec. Known bits were added to the set partitioning in hierarchical trees （SPIHT） coded image sequence periodically and directly. They were thought to be reliable information for C-VA in the decoder. Experimental results show that the proposed scheme can obtain much better error resilient ability compared with conventional VA under the extremely inferior channel condition if the best desired quality of reconstructed images can be sacrificed.

Linear algorithm for lexicographic enumeration of CFG parse trees

We study CFG parse tree enumeration in this paper. By dividing the set of all parse trees into infinite hierarchies according to height of parse tree, the hierarchical lexicographic order on the set of parse trees is established. Then grammar-based algorithms for counting and enumerating CFG parse trees in this order are presented. To generate a parse tree of height n, the time complexity is O（n）. If τ is a lowest parse tree for its yield, then O（n） =O（｜｜τ｜｜ ＋ 1）, where ｜｜τ｜｜ is the length of the sentence （yield） generated by τ. The sentence can be obtained as a by-product of the parse tree. To compute sentence from its parse tree （needn＇t be lowest one）, the time complexity is O（node）＋O（｜｜τ｜｜ ＋ 1）, where node is the number of non-leaf nodes of parse tree τ. To generate both a complete lowest parse tree and its yield at the same time, the time complexity is O（｜｜τ｜｜ ＋ 1）.