There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Set partition coding (SPC) has shown tremendous success in image compression. Despite its popularity, the lack of error resilience remains a significant challenge to the transmission of images in error-prone environments. In this paper, we propose a novel data representation called the progressive significance map (prog-sig-map) for error-resilient SPC. It structures the significance map (sig-map) into two parts: a high-level summation sig-map and a low-level complementary sig-map (comp-sig-map). Such a structured representation of the sig-map allows us to improve its error-resilient property at the price of only a slight sacrifice in compression efficiency. For example, we have found that a fixed-length coding of the comp-sig-map in the prog-sig-map renders 64% of the coded bitstream insensitive to bit errors, compared with 40% with that of the conventional sig-map. Simulation results have shown that the prog-sig-map can achieve highly competitive rate-distortion performance for binary symmetric channels while maintaining low computational complexity. Moreover, we note that prog-sig-map is complementary to existing independent packetization and channel-coding-based error-resilient approaches and readily lends itself to other source coding applications such as distributed video coding.

Progressive Significance Map and Its Application to Error-Resilient Image Transmission

Based on the set positioning in hierarchical tree (SPIHT) algorithm, fast seismic data compression based on the high-efficiency SPIHT (HESPIHT) algorithm is presented. To verify the validity of the algorithm, 10 seismic cross-sections are selected for the experiment. The result shows that the algorithm can reserve the quality of data better, meanwhile improving the efficiency of encoding and decoding.

Fast seismic data compression based on high-efficiency SPIHT

Motion differential set partition coding for image sequence and video compression

In recent years, researchers are paying much attention towards the video compression techniques due to the increasing need of storing huge video information in less storage space. H.264 is a popular algorithm for video compression, but it requires more attention towards its performance to improve the visual quality and the compression rate. In literature, there are several algorithms for video compression by providing a good motion computation scheme which is a crucial part of H.264. But these techniques affect the visual quality and the compression rate of the video. By considering this, two important contributions are presented in this paper. The first contribution is a new motion compensation technique through adaptive assisted block search algorithm. The second contribution is devising of new objective function for selecting the best blocks handling rate-distortion tradeoffs. Accordingly, Adaptive Shape Assisted Block Search Algorithm and fuzzy holoentropy-enabled cost function are developed for motion vector computation. The performance analysis is done using two metrics such as Peak Signal Noise Ratio and Compression Ratio to prove the visual quality and compression. Five different video are used for the experimentation and the result shows that the proposed algorithm attained the highest PSNR of 41 dB when compared with elastic model-based compression and H.264.

ASABSA: Adaptive Shape Assisted Block Search Algorithm and Fuzzy Holoentropy-Enabled Cost Function for Motion Vector Computation

Efficient image sequence coding exploits both spatial correlation and temporal correlation SPIHT is a powerful algorithm in exploiting spatial correlations for still image coding Based on SPIHT, we present a novel approach to exploit temporal correlations for image sequence coding, while maintaining single frame, random access decoding The so-called Differential-SPIHT takes advantage of inter-frame correlations by reusing the significance testing data of a SPIHT coded frame From simulation results of videos and volumetric medical images, Differential-SPIHT offers significant reductions in bitrate from conventional two-dimensional (2D) SPIHT for the same reconstruction PSNR, while retaining the desirables features of rate scalability and computational simplicity

Differential-SPIHT for image sequence coding

A method, computer system, and a computer program product is disclosed for encoding a sequence of color frames. The method includes a processor obtaining a sequence of color frames and rendering a first frame of the sequence in at least three components, each component representing a different color value. For each of the at least three components, the processor performs a wavelet transform on the first frame, initializes a significant points list and a list of insignificant sets to create an individual spatial tree of the list of insignificant sets for each component, searches all of the at least three components to identify a most significant bit in the first frame, and creates a consolidated significance map with all the color components for the first frame by searching the individual spatial tree for each component. The processor then obtains this significance map and utilizes the significance map to encode the first frame. The processor retains the significance map in memory as a key frame significance map and retains the first frame, or a color transform of the first frame, in memory, as a key frame.

Motion differential set partition coding for color image sequence compression

A method, computer system, and a computer program product is disclosed for encoding a sequence of frames as one or more compressed bitstreams, the method includes a processor obtaining a sequence of frames in an order and performing a wavelet transform on each frame of the sequence of frames independently in the order. The processor constructs a significant points list and an insignificant sets list, creating one or more spatial trees comprised of branch nodes of the list of insignificant sets for each frame of the sequence of frames. The processor initializes the significant points list and the list of insignificant sets for each frame and identifies a most significant bit in each frame and for each frame, selects at least one coding unit and creates a progressive significance map for coding. The processor writes a global header and a local header for the compressed bitstreams for each coding unit.

Yang Hu

Papers

Progressive Significance Map and Its Application to Error-Resilient Image Transmission

Motion differential set partition coding for image sequence and video compression

Differential-SPIHT for image sequence coding

Motion differential set partition coding for color image sequence compression

Error-resilient coder of image sequences and video