In this paper we present a general formalism for the establishment of the family of SELECTIVE PARTIAL UPDATE affine projection algorithms (SPU-APA). The SPU-APA, the SPU regularized APA (SPU-R-APA), the SPU PARTIAL rank algorithm (SPU-PRA), the SPU binormalized data reusing least mean squares (SPU-BNDR-LMS), and the SPU normalized LMS with orthogonal correction factors (SPU-NLMS-OCF) algorithms are established by this general formalism. In these algorithms, the filter coefficients are PARTIALly UPDATEd rather than the entire filter coefficients at every iteration which is computationally efficient. Following this, the transient and steady-state performance analysis of this family of adaptive filter algorithms are studied. This analysis is based on energy conservation arguments and does not need to assume a Gaussian or white distribution for the regressors. We demonstrate the performance of the presented algorithms through simulations in system identification and acoustic echo cancellation scenarios. The good agreement between theoretically predicted and actually observed performances is also demonstrated.

In this paper we show how the classical and modern adaptive filter algorithms can be introduced in a unified way. The Max normalized least mean squares (MAX-NLMS), N-Max NLMS, the family of SPU-NLMS, SPU transform domain adaptive filter (SPU-TDAF), and SPU subband adaptive filter (SPU-SAF) are particular algorithms are established in a unified way. Following this, the concept of set-membership (SM) adaptive filtering is extended to this framework, and a unified approach to derivation of SM and SM-SPU adaptive filters is presented. The SM-NLMS, SM-TDAF, SM-SAF, SM-SPU-NLMS, and SM-SPUSAF are presented based on this approach. Also, this concept is extended to the SPU affine projection (SPU-AP) and SPUTDAF algorithms and two new algorithms which are called SM-SPU-AP and SM-SPU-TDAF algorithms, are established. These novel algorithms are computationally efficient. The good performance of the presented algorithms is demonstrated in system identification application.

SELECTIVE PARTIAL UPDATE (SPU) strategy in adaptive filter algorithms is used to reduce the computational complexity. In this paper we apply the SPU normalized least mean squares algorithm (SPU-NLMS) for distributed estimation problem in an incremental network. The distributed SPU-NLMS (dSPU-NLMS) has close convergence speed to dNLMS, low steady-state mean square error (MSE), and low computational complexity features. In addition, the mean-square performance analysis of dSPU-NLMS algorithm for each individual node is presented. The theoretical expressions for stability bounds, transient and steady-state performance analysis of dSPU-NLMS are introduced. The validity of the theoretical results and the good performance of dSPU-NLMS are demonstrated by several computer simulations.

This paper presents a family of Variable Step-Size (VSS) Affine Projection (AP) adaptive filtering algorithms with SELECTIVE PARTIAL UPDATEs (SPU) and SELECTIVE Regressors (SR). The presented algorithms have good convergence speed, low steady state Mean Square Error (MSE), and low computational complexity features. The stability bounds of the family of SPU-APA, SR-APA and SPU-SR-APA are analyzed, based on the energy conservation arguments. This analysis does not need to assume a Gaussian or white distribution for the regressors. We demonstrate the good performance of the proposed algorithms through simulations in system identification and acoustic echo cancellation scenarios.

Two-dimensional (2D) adaptive filtering is a technique that can be applied to many image and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to 2D structure and the novel 2D adaptive filters are established. Based on this extension, the 2D variable step-size normalized least mean squares (2D-VSSNLMS), the 2D-VSS affine projection algorithms (2D-VSS-APA), the 2D set-membership NLMS (2D-SM-NLMS), the 2D-SM-APA, the 2D SELECTIVE PARTIAL UPDATE NLMS (2DSPU- NLMS), and the 2D-SPU-APA are presented. In 2D-VSS adaptive filters, the stepsize changes during the adaptation which leads to improve the performance of the algorithms. In 2D-SM adaptive filter algorithms, the filter coefficients are not UPDATEd at each iteration. Therefore, the computational complexity is reduced. In 2D-SPU adaptive algorithms, the filter coefficients are PARTIALly UPDATEd which reduce the computational complexity. We demonstrate the good performance of the proposed algorithms thorough several simulation results in 2D adaptive noise cancellation (2D-ANC) for image denoising. The results are compared with the classical 2D adaptive filters such as 2D-LMS, 2D-NLMS, and 2D-APA.

This paper presents a new Variable Step-Size Normalized Subband Adaptive Filter (VSS-NSAF) algorithm. The proposed algorithm uses the prior knowledge of the system impulse response statistics and the optimal step-size vector is obtained by minimizing the Mean-Square Deviation (MSD). In comparison with NSAF, the VSS-NSAF algorithm has faster convergence speed and lower MSD. To reduce the computational complexity of VSS-NSAF, the VSS SELECTIVE PARTIAL UPDATE NSAF (VSS-SPU-NSAF) is proposed where the filter coefficients are PARTIALly UPDATEd in each subband at every iteration. We demonstrated the good performance of the proposed algorithms in convergence speed and steady-state MSD for a system identification set-up.