EOG removal using regression

The current version of the toolbox (v1.3) includes four adaptive algorithms for EOG removal using one or more EOG regression channels. The implementations of those algorithms are not optimized for speed so you should expect a relatively large computation time. The first algorithm is based on classical Least Mean Squares (LMS) [10], which is very simple and quite stable if a small enough learning step is used. However, small learning steps lead to very slow convergence. The second algorithm is based on Recursive Least Squares (RLS) [10] which offers a much greater convergence speed at the cost of reduced numerical stability. The third algorithm is a numerically stable version of the RLS algorithm [15]. Note that the implementation of this latter algorithm is still very naive and inefficient so the required computation time can be very large. The two last algorithms are based on $H^{\infty }$ principles [17,18]. The most important information related to these regression algorithms is summarized in Table. 1.

Table 1: The regression algorithms in a nutshell

Algorithm	MATLAB files	Ref.	Strengths	Weaknesses
LMS	lms_regression	[10]	Simplicity	Slow conv.
	pop_lms_regression		Stability
RLS	crls_regression	[11]	Fast conv.	Unstability
	pop_crls_regression
Stable	scrls_regression	[15]	Fast conv.	Comp. time
RLS	pop_scrls_regression		Stability
$H^{\infty }$	hinftv_regression	[17]	Fast conv.	Unstability
	pop_hinftv_regression		Accuracy	Comp. time
	hinfew_regression
	pop_hinfew_regression