Fast algorithm for the 3-D DCT-II

Recently, many applications for three-dimensional (3-D) image and video compression have been proposed using 3-D discrete cosine transforms (3-D DCTs). Among different types of DCTs, the type-II DCT (DCT-II) is the most used. In order to use the 3-D DCTs in practical applications, fast 3-D algorithms are essential. Therefore, in this paper, the 3-D vector-radix decimation-in-frequency (3-D VR DIF) algorithm that calculates the 3-D DCT-II directly is introduced. The mathematical analysis and the implementation of the developed algorithm are presented, showing that this algorithm possesses a regular structure, can be implemented in-place for efficient use of memory, and is faster than the conventional row-column-frame (RCF) approach. Furthermore, an application of 3-D video compression-based 3-D DCT-II is implemented using the 3-D new algorithm. This has led to a substantial speed improvement for 3-D DCT-II-based compression systems and proved the validity of the developed algorithm

Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for DCTs and DSTs

This paper presents a systematic methodology based on the algebraic theory of signal processing to classify and derive fast algorithms for linear transforms. Instead of manipulating the entries of transform matrices, our approach derives the algorithms by stepwise decomposition of the associated signal models, or polynomial algebras. This decomposition is based on two generic methods or algebraic principles that generalize the well-known Cooley-Tukey FFT and make the algorithms' derivations concise and transparent. Application to the 16 discrete cosine and sine transforms yields a large class of fast algorithms, many of which have not been found before.Comment: 31 pages, more information at http://www.ece.cmu.edu/~smar

A simple algorithm for decoding Reed-Solomon codes and its relation to the Welch-Berlekamp algorithm

A simple and natural Gao algorithm for decoding algebraic codes is described. Its relation to the Welch-Berlekamp and Euclidean algorithms is given.Comment: 7 pages. Submitted to IEEE Transactions on Information Theor

Computationally effective range migration compensation in PCL systems for maritime surveillance

In this paper, we consider the possibility of extending the coherent processing interval (CPI) as a way to improve target detection capability in passive radars for maritime surveillance applications. Despite the low velocity of the considered targets, range walk effects could limit the performance of the system when long CPIs are considered. To overcome these limitations while keeping the computational load controlled, we resort to a sub-optimal implementation of the Keystone Transform (KT), based on Lagrange polynomial interpolation, recently presented by the authors and successfully applied against aerial targets. Following those promising results, we extend the proposed approach to a coastal surveillance scenario. In the considered case, since longer CPI values are used, the proposed strategy appears to be even more attractive with respect to a conventional KT implementation based on the Chirp-Z Transform interpolation. In fact, comparable detection performance are obtained with a remarkable computational load saving. In detail, the effectiveness of the proposed approach is demonstrated against experimental data provided by Leonardo S.p.A., using a DVB-T based passive radar