Improved Integer Transforms Using Multi-dimensional Lifting
نویسندگان
چکیده
Recently lifting-based integer transforms have received much attention, especially in the area of lossless audio and image coding. The usual approach is to apply the lifting scheme to each Givens rotation. Especially in the case of long transform sizes in audio coding applications, this leads to a considerable approximation error in the frequency domain. This paper presents a multidimensional lifting approach for reducing this approximation error. In this approach, large parts of the transform are calculated without rounding operations, only the output is rounded and added. The new approach is applied and evaluated for both the Integer Modified Discrete Cosine Transform (IntMDCT) and the Integer Fast Fourier Transform (IntFFT).
منابع مشابه
Non-separable 3D integer wavelet transform for lossless data compression
This paper proposes a three-dimensional (3D) integer wavelet transform with reduced amount of rounding noise. Non-separable multi-dimensional lifting structures are introduced to decrease the total number of lifting steps. Since the lifting step contains a rounding operation, variance of the rounding noise generated due to the rounding operation inside the transform is reduced. This paper also ...
متن کاملImproved Integer Transforms for Lossless Audio Coding
Lifting scheme based integer transforms are very powerful tools to construct lossless coding schemes. These transforms such as the Integer Fast Fourier Transform (IntFFT) and the Integer Modified Discrete Cosine Transform (IntMDCT) are integer approximations of the original floatingpoint transforms, and hence there is an approximation error in the transform domain. This paper will propose struc...
متن کاملLossless Image Compression Using Integer to Integer Wavelet Transforms
Invertible wavelet transforms that map integers to integers are important for lossless representations. In this paper, we present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless im...
متن کاملInteger Wavelet Transforms using the Lifting Scheme
Due to its good decorrelating properties, the wavelet transform is a powerful tool for signal analysis. The lifting scheme is an efficient algorithm to calculate wavelet transforms and it allows for the construction of second-generation wavelets. Furthermore it can easily be converted to an integer transform, which is of great importance for multimedia applications. We show how the lifting sche...
متن کاملProjection-based Context Modeling for Reversible Integer Wavelet Transforms
Reversible integer wavelet transforms are increasingly popular in lossless image compression, as evidenced by their use in the recently developed JPEG2000 image coding standard 1]. In this paper, a projection technique is described that exploits non-orthogonality among transform basis vectors to derive nal lifting steps for wavelet transforms. Additionally , projection-based predictions of deta...
متن کامل