The paper shows how to convert the order-8 cosine transforms into a family of integer cosine transforms (ICTs) using the theory of dyadic symmetry. The new transforms can be implemented using simple integer arithmetic. It was found that performance close to that of the DCT can be achieved with an ICT that requires only 4 bits for representation of its kernel com- ponent magnitude. Better performance can be achieved by some ICTs whose kernel components require longer bit lengths for representation. ICTs that require 3 bits or less for representation of their component magnitude are available but with degraded performance. The availability of many ICTs provides an engineer the freedom to tradeoff performance for simple implementation in design- ing a transform codec.

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Development of integer cosine transforms by the principle of dyadic symmetry

For joint image compression and encryption schemes, the encryption power and compression efficiency are commonly two contradictory things. In this paper, we propose a new joint image compression and encryption scheme based on a lossy JPEG standard, which aims at encryption power's enhancement, on the premise of maintaining the JPEG's compression efficiency. The proposed scheme is image-content-adaptive, since the secret encryption key is generated from the plain image using the BLAKE2 hash algorithm. Three encryption operations are contained in our scheme, alternating new orthogonal transforms transformation, dc coefficients encryption, and ac coefficients encryption. To save the cost for transmitting different encryption keys each time to decoder for decryption when the plain image changes, we propose embedding the encryption key into the entropy-encoded bitstream of some ac coefficients, and the whole embedding procedure is controlled by another secret key called the embedding key. Extensive experiments are conducted to show that our encryption scheme is JPEG friendly, and has good confusion and diffusion properties. Detailed security analysis is also given to illustrate the proposed scheme's persistence to various cryptanalysis strategies.

A Content-Adaptive Joint Image Compression and Encryption Scheme

A new integer image coding technique based on orthogonal polynomials

The sine and cosine transforms, which are popular transforms for image coding, are members of a sinusoidal transform family. Each member of the family is the optimal KLT of a Markov process. This paper derives the conditions under which the order-8 sinusoidal transforms can be approximated by orthogonal integer transforms which can be implemented using integer arithmetic. Some integer transforms are derived as examples. The results show that for the popular even sine-1, even sine-2 and the cosine transforms, there is an infinite number of integer transforms and some have their transform component magnitudes less than eight. In LSI implementation, if low implementation cost and fast computation speed are paramount, then an integer transform of small component magnitudes can be chosen. If better performance is desired, integer transforms whose elements have larger magnitudes can be used. The availability of many integer transforms provides a design engineer the freedom to trade-off performance against simpl...

Integer sinusoidal transforms for image processing

This paper presents the history of international standardization activities and specifications relating to the precision of
inverse discrete cosine transform (IDCT) approximations used in video compression designs. The evolution of issues
relating to IDCT precision and the "drift" effects of IDCT mismatch between encoder modeling of decoder behavior is
traced, starting with the initial requirements specified for ITU-T H.261 and continuing through the MPEG-1,
H.262/MPEG-2, H.263, MPEG-4 Part 2, and H.264/MPEG-4 Part 10 AVC projects. Finally, the development of the new
MPEG-C Part 1 and Part 2 standards is presented. MPEG-C Part 1 contains a centralized repository for specification of
IDCT precision conformance requirements for the various MPEG video coding standards prior to MPEG-4 Part 10.
MPEG-C Part 2 specifies one particular IDCT approximation for adoption in industry implementations of existing
standards. The use of MPEG-C Part 2 by encoders can eliminate IDCT mismatch drift error when decoded using an
MPEG-C Part 2 conforming decoder, resulting in a deterministic decoded result. MPEG-C Part 2 also provides an
example for guiding implementers on how to design a decoder with high precision and without excessive computational
resource requirements.

Standardization of IDCT approximation behavior for video compression: the history and the new MPEG-C parts 1 and 2 standards

Two new transforms which can be used as substitutes for the Walsh transform are generated using the theory of dyadic symmetry. The new transforms have virtually the same complexity and computational requirements as the Walsh transform, employing additions, subtractions and binary shifts only, but have an efficiency, defined in terms of their ability to decorrelate signal data, which lies between that of the Walsh transform and that of the discrete cosine transform.

W.K. Cham

Papers

Application of the principle of dyadic symmetry to the generation of orthogonal transforms