Block Recursive Algorithm Research Articles

The generalized frequency-domain adaptive filtering algorithm as an approximation of the block recursive least-squares algorithm

Acoustic echo cancellation (AEC) is a well-known application of adaptive filters in communication acoustics. To implement AEC for multichannel reproduction systems, powerful adaptation algorithms like the generalized frequency-domain adaptive filtering (GFDAF) algorithm are required for satisfactory convergence behavior. In this paper, the GFDAF algorithm is rigorously derived as an approximation of the block recursive least-squares (RLS) algorithm. Thereby, the original formulation of the GFDAF algorithm is generalized while avoiding an error that has been in the original derivation. The presented algorithm formulation is applied to pruned transform-domain loudspeaker-enclosure-microphone models in a mathematically consistent manner. Such pruned models have recently been proposed to cope with the tremendous computational demands of massive multichannel AEC. Beyond its generalization, a regularization of the GFDAF is shown to have a close relation to the well-known block least-mean-squares algorithm.

Spark-Based Large-Scale Matrix Inversion for Big Data Processing

Matrix inversion is a fundamental operation for solving linear equations for many computational applications, especially for various emerging big data applications. However, it is a challenging task to invert large-scale matrices of extremely high order (several thousands or millions), which are common in most Web-scale systems, such as social networks and recommendation systems. In this paper, we present an lower upper decomposition-based block-recursive algorithm for large-scale matrix inversion. We present its well-designed implementation with optimized data structure, reduction of space complexity, and effective matrix multiplication on the Spark parallel computing platform. The experimental evaluation results show that the proposed algorithm is efficient to invert large-scale matrices on a cluster composed of commodity servers and is scalable for inverting even larger matrices. The proposed algorithm and implementation will become a solid foundation for building a high-performance linear algebra library on Spark for big data processing and applications.

Design and Optimization of an HSDPA Turbo Decoder ASIC

The turbo decoder is the most challenging component in a digital HSDPA receiver in terms of computation requirement and power consumption, where large block size and recursive algorithm prevent pipelining or parallelism to be effectively deployed. This paper addresses the complexity and power consumption issues at algorithmic, arithmetic and gate levels of ASIC design, in order to bring power consumption and die area of turbo decoders to a level commensurate with wireless application. Realized in 0.13 nmum CMOS technology, the turbo decoder ASIC measures 1.2nmm2 excluding pads, and can achieve 10.8 Mb/s throughput while consuming only 32 mW.

Efficient algorithms for estimating the general linear model

Computationally efficient serial and parallel algorithms for estimating the general linear model are proposed. The sequential block-recursive algorithm is an adaptation of a known Givens strategy that has as a main component the Generalized QR decomposition. The proposed algorithm is based on orthogonal transformations and exploits the triangular structure of the Cholesky QRD factor of the variance–covariance matrix. Specifically, it computes the estimator of the general linear model by solving recursively a series of smaller and smaller generalized linear least squares problems. The new algorithm is found to outperform significantly the corresponding LAPACK routine. A parallel version of the new sequential algorithm which utilizes an efficient distribution of the matrices over the processors and has low inter-processor communication is developed. The theoretical computational complexity of the parallel algorithms is derived and analyzed. Experimental results are presented which confirm the theoretical analysis. The parallel strategy is found to be scalable and highly efficient for estimating large-scale general linear estimation problems.

Combinative motion estimation algorithm and the corresponding architecture for complex motion phenomenon

By combining the features of block matching algorithm and block recursive algorithm a new motion estimation method is proposed for the complex motion phenomenon. With the full searching procedure used in the block matching algorithm and the adaptive searching procedure used in the block recursive algorithm, the proposed combinative algorithm can estimate more complex motion parameters such as translation, zoom, rotation and image deformation resulting in a good performance. To reduce the computational complexity, the corresponding architecture of the combinative algorithm is also proposed. With this architecture the computation requirements can be largely reduced to make the proposed algorithm suitable for real time motion estimation.

Recursive PLS algorithms for adaptive data modeling

Partial least squares (PLS) regression is effectively used in process modeling and monitoring to deal with a large number of variables with collinearity. In this paper, several recursive partial least squares (RPLS) algorithms are proposed for on-line process modeling to adapt process changes and off-line modeling to deal with a large number of data samples. A block-wise RPLS algorithm is proposed with a moving window and forgetting factor adaptation schemes. The block-wise RPLS algorithm is also used off-line to reduce computation time and computer memory usage in PLS regression and cross-validation. As a natural extension, the recursive algorithm is extended to dynamic modeling and nonlinear modeling. An application of the block recursive PLS algorithm to a catalytic reformer is presented to adapt the model based on new data.

Architectural Study of a Block-Recursive Motion Estimation Algorithm

The block-recursive algorithm for motion estimation is an option to classical methods like block-matching usually used in conventional coding schemes based on motion compensation. The block-recursive algorithm considered in this study as been developed at IRISA in the Temis group. It is composed of three steps: estimation, deterministic relaxation, and quadtree region splitting. These steps are iteratively executed until convergence.To be fully exploitable, a specialized VLSI architecture for motion estimation must satisfy the following features: real-time performance, modularity, easy external interfacing, flexibility and reduced internal complexity. In this paper, we analyse these different features with regards to the numerous parameters of the considered block-recursive algorithm. The influence of parameters on the quality of the coding algorithm is measured through numerous simulations. Architectural mechanisms required for an efficient implementation are also presented and discussed. This study falls within the framework for derivation of a specialized parallel architecture from the initial sequential algorithm specification.

Motion parameter estimation based on the block recursive algorithm with finite word length

A three parameter motion model can better describe the motion trajectory of the picture element in a video sequence. Combining the features of the block process and recursive estimation, a block recursive algorithm is proposed to calculate these three motion parameters with compensation for the variety of block positions to get a better stability. To simplify the hardware implementation requirements, the representation accuracy of the displaced frame difference and gradient that are given is analyzed. From this analysis we propose a quantized block recursive algorithm with quantized gradient to reduce the computational complexity. With this simplification the quantized motion estimation algorithm has a sufficient computational speed to meet the requirement of real time application with the least accuracy loss.

Block recursive algorithm to generate Jacobi-sets

The pairs in the set {( i, j)∥ 1 ⩽ i < j ⩽ n} can be distributed into ( n − 1) sets, such that each set contains exactly n/2 disjoint pairs. We refer to these ( n−1) sets as complete Jacobi-sets. Gao and Thomas have [4] developed a recursive algorithm for exchanges of elements on a hypercube configuration to generate complete Jacobi sets. Inspired by the algorithm we present a block recursive algorithm to generate these sets continuously and return to its initial state after the last Jacobi set has been generated. In the process of the derivation of the BR algorithm, we developed some interesting combinatorial properties on the hypercube topology related to the Jacobi-sets. We include those results in this paper. An important application of the Jacobi-sets lies in the parallel implementation for Jacobi-type methods. The order in which the pairs ( i, j) are chosen is important in defining these algorithms. We present in this paper a study on the effect of different orderings on the convergence of Jacobi-type methods. Our tests indicate that the ordering defined by our block recursive algorithm is as good as the odd-even ordering.