This paper presents a method for encrypting JPEGcoded images that preserves both compression ratio and format of a bit stream.Such solutions allow for selectively hiding information: image contents can be encrypted, while in-file metadata remain readable.Our algorithm is a symmetric, polygram substitution cipher, as it replaces Huffman code words and rearranges value bits that describe the main results of the Discrete Cosine Transform (DCT) of a pixel block: the DC coefficient and the first non-zero AC coefficient.Both length and format of a file are preserved, because bits are modified under constraints on their numbers.Such encryption is a kind of post-processing of a compressed bit stream, and thus it can be built on the top of an existing JPEG codec, without accessing its internals.Compared to previous similar solutions, our approach better hides image contours, exchanging AC for DC energy.Our work also reveals some properties of Huffman code tables and bit streams related to the JPEG standard.

Novel 4D CORDIC algorithms and hardware architecture for multiplying quaternions are presented, aimed at constant-coefficient multipliers. In our solution, microrotations are multiplications by hypercomplex numbers with only one non-zero imaginary part. Such transformations can be described using sparse matrices and implemented using less hardware resources than the iteration of the known quaternion CORDIC algorithm. Chip area can be saved because sparse microrotations can be computed using a permutation network and two-operand adders, without four-operand additions, which are necessary in the known solution. The obtainable area savings depend on the implementation technology and the architectures of adders and bit shifters but can be as large as 45 and 25 percent for ASIC and FPGA circuits, respectively. The circuitry simplifications come at the cost of slowing down computations: our approach improves the area-delay product, and a single sparse iteration can be executed up to 15 percent faster than the conventional one, but more microrotations are usually necessary to achieve the required accuracy. On the other hand, a sparse 4D iteration can be identified with microrotations of two 2D CORDICs which work in parallel. This makes convergence analysis easier than in the previous 4D solution, as it is sufficient to consider only two dimensions.

The aim of this paper is to evaluate the cosine-sine (CS) decomposition as a means for computing the 8-point Discrete Cosine Transform (DCT). By iteratively decomposing matrices after reordering their columns or rows, novel factorizations of the DCT matrix have been obtained that describe interesting algorithms for computing the transform. Some of them are only characterized by regular, symmetric data-flows, whereas others require a few computations. This suggests that our method can be used to search for innovative algorithms for other block transforms and to optimize hardware implementations.

This paper shows that the principles of video coding that are related to removing temporal redundancy by means of motion estimation and compensation can be successfully used to compress still images. If all polyphase components of an image are identified with correlated video frames, only one of them needs to be intra-coded, as the rest can be encoded using mainly bidirectional prediction. Using the H.264 reference software, it has been experimentally verified that the approach offers compression comparable to intra-coding the whole image as a single video frame, the common way of applying the H.264 standard to still pictures. As the H.264 encoder is not optimized for processing polyphase components, the results suggest that, based on the presented idea, it is possible to develop a new image codec that could compete with the state-of-art algorithms.

A simple directional extension of the JPEG standard is proposed, which consists in rearranging pixels in 8 × 8 blocks before the DCT-based transform coding, and then restoring the original pixel positions before putting reconstructed blocks into the decoded image buffer. Pixels are shuffled so as to improve block reconstruction accuracy and/or to decrease the number of bits to be put into a JPEG-compliant bit stream. For numerous pictures, such a straightforward adapting a signal to a transform gives evident gains in compression efficiency over the original JPEG. Even though the more advanced known algorithms offer better results, the presented solution requires less computations and memory and is more hardware friendly.

This paper presents a novel approach to the finite precision implementation of the eight point discrete cosine transform (DCT). Two multiplierless computational schemes of the plane rotation block are constructed to obtain the transform approximations maintaining orthogonality regardless of their coefficient quantization. This is the main difference with respect to the solutions based on lifting schemes being developed in recent years, characterized by inherent biorthogonality. In our technique, structural orthogonality comes at the cost of a complexity increase. To keep it at a moderate level, we implement rotations effectively using the denormalized lattice and the three-value coordinate rotation digital computer (CORDIC) algorithm with double mu-rotations

This paper investigates the first regularity of the three main subclasses of four-band paraunitary filter banks (PUFBs): general, linear phase and those with pairwise-mirror-image (PMI) properties. It is considered from the perspective of quaternionic lattice structures known to maintain their orthogonality regardless of coefficient quantization. This approach turns out to be very useful anew, as the first regularity can be very straightforwardly expressed in terms of quaternionic lattice coefficients. Moreover, the property can be easily preserved in finite precision implementations, what is demonstrated by appropriate design examples

We consider the warped DFT as an alternative basis for psychoacoustic models. The appropriate construction of the transform is approached, aiming for precise critical band power analysis. It is shown that sufficient spectral resolution can be obtained for sample block lengths several times shorter than the 1024 or 2048 commonly used in the FFT based ear models. Thus, temporal resolution is improved and comparable with that of more complex perceptual models utilizing filter banks. The computational complexity is estimated as acceptable for realtime processing.