Block-diagonal structure of Walsh-Hadamard/discrete cosine transform

The A-matrix, the conversion matrix for Walsh-Hadamard/discrete cosine transform, is known for its efficient block-diagonal structure. This associates with the even/odd structure of the transform kernels. In the letter we present a direct matrix derivation by using the intrinsic properties of the discrete cosine transform and the Walsh-Hadamard transform.     

Real-time software-based video coder for multimedia communication systems

A novel software-based video compression algorithm, the Popular Video Coder (PVC), is presented in this paper, and a video phone system, the Popular Phone, is also implemented based on the PVC. The PVC simplifies the traditional video coder by removing the transform and the motion estimation parts and modifies the quantizer and entropy coder. Two novel coding algorithms, the adaptive quantizer and the modified windowed Huffman-like coder, are used in the PVC to encode the video data with a quality picture at a high compression ratio. The video quality of the proposed coder is as good as that of the MPEG coder when the input is a low-resolution and slow-motion video, and the computational complexity of the PVC is much lower than that of the Motion Picture Expert Group (MPEG). Since no compression hardware is needed for the PVC to encode and decode video data, the cost and complexity of developing multimedia applications, such as video phone and multimedia e-mail systems, can be greatly reduced. Furthermore, some networking issues, such as error control and flow control, are discussed in connection with applying the PVC to implement the Popular Phone.     

Direct splitting and merging of 2-D DCT in the DCT domain

An efficient method for splitting an 8×8 2-D DCT block into four 4×4, two 8×4 (or 4×8) 2-D DCT blocks is presented in this paper. The reverse direction (the “merge” case) also can be realized by inverse transposing the given matrix operations in the “split” case. The computational complexity of the proposed methods is lower than that of the direct approach and other known efficient converting approaches. Due to its efficiency, the proposed DCT splitter/merger will play an important role in realizing the transcoding between the latest video coding standard, AVC/H.264, and the older ones, such as MPEG-1, MPEG-2, and MPEG-4 part 2.     

On constructing the Huffman-code-based reversible variable-lengthcodes

In this letter, we propose a generic and efficient algorithm that can construct both asymmetrical and symmetrical reversible variable-length codes (RVLCs). Starting from a given Huffman code, the construction is based on two developed codeword selection mechanisms, for the symmetrical case and the asymmetrical case, respectively; it is shown that the two mechanisms possess simple features and can generate efficient RVLCs easily. In addition, two new asymmetrical RVLCs are constructed and shown to be very efficient for further reducing the coding overheads in MPEG-4 when operating in the reversible decoding mode     

Attacking visible watermarking schemes

Visible watermarking schemes are important intellectual property rights (IPR) protection mechanisms for digital images and videos that have to be released for certain purposes but illegal reproductions of them are prohibited. Visible watermarking techniques protect digital contents in a more active manner, which is quite different from the invisible watermarking techniques. Digital data embedded with visible watermarks will contain recognizable but unobtrusive copyright patterns, and the details of the host data should still exist. The embedded pattern of a useful visible watermarking scheme should be difficult or even impossible to be removed unless intensive and expensive human labors are involved. In this paper, we propose an attacking scheme against current visible image watermarking techniques. After manually selecting the watermarked areas, only few human interventions are required. For watermarks purely composed of thin patterns, basic image recovery techniques can completely remove the embedded patterns. For more general watermarks consisting of thick patterns, not only information in surrounding unmarked areas but also information within watermarked areas will be utilized to correctly recover the host image. Although the proposed scheme does not guarantee that the recovered images will be exactly identical to the unmarked originals, the structure of the embedded pattern will be seriously destroyed and a perceptually satisfying recovered image can be obtained. In other words, a general attacking scheme based on the contradictive requirements of current visible watermarking techniques is worked out. Thus, the robustness of current visible watermarking schemes for digital images is doubtful and needs to be improved.     

Class of majority decodable real-number codes

A majority decoding algorithm for a class of real-number codes is presented. Majority decoding has been a relatively simple and fast decoding technique for codes over finite fields. When applied to decode real-number codes, the robustness of the majority decoding to the presence of background noise, which is usually an annoying problem for existing decoding algorithms for real-number codes, is its most prominent property. The presented class of real-number codes has generator matrices similar to those of the binary Reed-Muller codes and is decoded by similar majority logic     

Discrete cosine transform in error control coding

The authors define a new class of real-number linear block codes using the discrete cosine transform (DCT). They also show that a subclass with a BCH-like structure can be defined and, therefore, encoding/decoding algorithms for BCH codes can be applied, A (16,10) DCT code is given as an example     

Two-dimensional polynomial residue number system

The polynomial residue number system (PRNS) has been considered as a useful tool for digital signal processing (DSP) since it can support parallel, carry-free, high speed arithmetic with minimum multiplication count provided that an appropriate modular ring is chosen. In this paper, the properties of two-dimensional (2-D) PRNS are investigated in detail. It is shown that in the 2-D PRNS system, the theoretical lower bound for multiplication count of polynomial products can be achieved in some carefully chosen ring. Application of the proposed 2-D PRNS for computing 2-D circular convolution, which involves intensive multiplication operations, is also presented.     

Fast biased polynomial transforms for two-dimensional convolutions

The fast biased polynomial transforms are defined directly on the ZN?1 ring instead of a conventional cyclotomic polynomial ring. Such biased polynomial transforms may be combined with very efficient fast FFT algorithms. Two-dimensional convolutions may be carried out without using the complicated Chinese remainder theorem, complex mapping and column-row reordering processes.