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Research article

A multi-band centroid contrastive reconstruction fusion network for motor imagery electroencephalogram signal decoding

  • Received: 11 October 2023 Revised: 01 November 2023 Accepted: 07 November 2023 Published: 15 November 2023
  • Motor imagery (MI) brain-computer interface (BCI) assist users in establishing direct communication between their brain and external devices by decoding the movement intention of human electroencephalogram (EEG) signals. However, cerebral cortical potentials are highly rhythmic and sub-band features, different experimental situations and subjects have different categories of semantic information in specific sample target spaces. Feature fusion can lead to more discriminative features, but simple fusion of features from different embedding spaces leading to the model global loss is not easily convergent and ignores the complementarity of features. Considering the similarity and category contribution of different sub-band features, we propose a multi-band centroid contrastive reconstruction fusion network (MB-CCRF). We obtain multi-band spatio-temporal features by frequency division, preserving the task-related rhythmic features of different EEG signals; use a multi-stream cross-layer connected convolutional network to perform a deep feature representation for each sub-band separately; propose a centroid contrastive reconstruction fusion module, which maps different sub-band and category features into the same shared embedding space by comparing with category prototypes, reconstructing the feature semantic structure to ensure that the global loss of the fused features converges more easily. Finally, we use a learning mechanism to model the similarity between channel features and use it as the weight of fused sub-band features, thus enhancing the more discriminative features, suppressing the useless features. The experimental accuracy is 79.96% in the BCI competition Ⅳ-Ⅱa dataset. Moreover, the classification effect of sub-band features of different subjects is verified by comparison tests, the category propensity of different sub-band features is verified by confusion matrix tests and the distribution in different classes of each sub-band feature and fused feature are showed by visual analysis, revealing the importance of different sub-band features for the EEG-based MI classification task.

    Citation: Jiacan Xu, Donglin Li, Peng Zhou, Chunsheng Li, Zinan Wang, Shenghao Tong. A multi-band centroid contrastive reconstruction fusion network for motor imagery electroencephalogram signal decoding[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20624-20647. doi: 10.3934/mbe.2023912

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  • Motor imagery (MI) brain-computer interface (BCI) assist users in establishing direct communication between their brain and external devices by decoding the movement intention of human electroencephalogram (EEG) signals. However, cerebral cortical potentials are highly rhythmic and sub-band features, different experimental situations and subjects have different categories of semantic information in specific sample target spaces. Feature fusion can lead to more discriminative features, but simple fusion of features from different embedding spaces leading to the model global loss is not easily convergent and ignores the complementarity of features. Considering the similarity and category contribution of different sub-band features, we propose a multi-band centroid contrastive reconstruction fusion network (MB-CCRF). We obtain multi-band spatio-temporal features by frequency division, preserving the task-related rhythmic features of different EEG signals; use a multi-stream cross-layer connected convolutional network to perform a deep feature representation for each sub-band separately; propose a centroid contrastive reconstruction fusion module, which maps different sub-band and category features into the same shared embedding space by comparing with category prototypes, reconstructing the feature semantic structure to ensure that the global loss of the fused features converges more easily. Finally, we use a learning mechanism to model the similarity between channel features and use it as the weight of fused sub-band features, thus enhancing the more discriminative features, suppressing the useless features. The experimental accuracy is 79.96% in the BCI competition Ⅳ-Ⅱa dataset. Moreover, the classification effect of sub-band features of different subjects is verified by comparison tests, the category propensity of different sub-band features is verified by confusion matrix tests and the distribution in different classes of each sub-band feature and fused feature are showed by visual analysis, revealing the importance of different sub-band features for the EEG-based MI classification task.



    In this article, we study the existence of infinitely many homoclinic solutions of the following fractional discrete p-Laplacian equations:

    (Δ1)spu(a)+V(a)|u(a)|p2u(a)=λf(a,u(a)),in Z, (1.1)

    where s(0,1) and p(1,) are fixed constants, V(a)R+, λ is a positive parameter, f(a,) is a continuous function for all aZ and (Δ1)sp is the fractional discrete p-Laplacian given by

    (Δ1)spu(a)=2bZ,ba|u(a)u(b)|p2(u(a)u(b))Ks,p(ab),in Z,

    where the discrete kernel Ks,p has the following property: There exist two constants 0<cs,pCs,p, such that

    {cs,p|d|1+psKs,p(d)Cs,p|d|1+ps,for alldZ{0};Ks,p(0)=0. (1.2)

    The fractional operator has received more attention recent decades because of its many applications in the real world. Many scholars have paid attention to this kind of problem, and have produced a lot of classical works, see for example [1,2,3]. As a classical fractional operator, the fractional Laplacian has wide applications in various fields such as optimization, population dynamics and so on. The fractional Laplacian on R can be defined for 0<s<1 and νC0(RN) as

    (Δ)sν(x)=CN,sP.V.RNν(x)ν(y)|xy|N+2sdy,xRN,

    where CN,s is a positive constant and P.V. denotes the Cauchy principle value. In various cases involving differential equations, the Laplace operator is replaced by either the fractional Laplace operator or other more general operators, and hence the existence results have been obtained by employing variational approaches, see for instance [4,5,6,7]. These alternative approaches have been found to offer improved descriptions of numerous phenomena observed in the natural world. Correspondingly, it is necessary to give some qualitative results by employing numerical analysis. The nonlocal feature of the fractional Laplacian is one of the important aspects to be considered in numerical methods, which makes it necessary to study the existence of solutions.

    Let ZH denote a grid of fixed size H>0 on R, i.e., ZH={Ha|aZ}. In [8], the definition of the fractional discrete Laplacian on ZH is given by

    (ΔH)sν(a)=bZ,ba(ν(a)ν(b))KHs(ab),

    where s(0,1), νs={ν:ZHR|ωZ|ν(ω)|(1+|ω|)1+2s<} and

    KHs(a)={4sΓ(1/2+s)π|Γ(s)|Γ(|a|s)H2sΓ(|a|+1+s),aZ{0},0,a=0.

    The above discrete kernel KHs has the following property: There exist two constants 0<csCs, such that for all aZ{0} there holds

    csH2s|a|1+2sKHs(a)CsH2s|a|1+2s.

    In [8], Ciaurri et al. also proved that if ν is bounded then lims1(ΔH)sν(a)=ΔHν(a), where ΔH is there discrete Laplacian on ZH, i.e.

    ΔHν(a)=1H2(ν(a+1)2ν(a)+ν(a1)).

    Moreover, under some suitable conditions and H0, the fractional Laplacian can be approximated by the fractional discrete Laplacian.

    Subsequently, let us give some existence results on the fractional difference equations. Xiang et al. [9] first investigated the fractional discrete Laplacian equations based on variational methods:

    {(Δ1)sν(a)+V(a)ν(a)=λf(a,ν(a)),foraZ,ν(a)0,as|a|, (1.3)

    where f(a,) is a continuous function for all aZ, λ>0, V(a)R+ and

    (Δ1)sν(a)=2bZ,ba(ν(a)ν(b))Ks(ab),in Z.

    Using the mountain pass theorem and Ekeland's variational principle under some suitable conditions, they obtained two homoclinic solutions for problem (1.3). It is evident that when p=2, the discrete fractional p-Laplace operator corresponds to the discrete fractional Laplace operator. After that, Ju et al. [10] studied the following fractional discrete p-Laplacian equations

    {(Δ1)spν(d)+V(d)|ν(d)|p2ν(d)=λa(d)|ν(d)|q2ν(d)+b(d)|ν(d)|r2ν(d),fordZ,ν(d)0,as|d|, (1.4)

    where appq, b, 1<q<p<r<, λ>0, V(a)R+, (Δ1)sp is the fractional discrete p-Laplacian. Under certain conditions, they employed the Nehari manifold method to achieve the existence of at least two homoclinic solutions for problem (1.4). In [11], Ju et al. investigated the existence of multiple solutions for the fractional discrete p-Laplacian equations with various nonlinear terms via different Clark's theorems. In a recent study conducted by Ju et al. in [12], it was demonstrated that using the fountain theorem and the dual fountain theorem under the same hypotheses, two separate sequences of homoclinic solutions were derived for the fractional discrete Kirchhoff-Schrödinger equations. Based on the findings from [8], it could be deduced that Eq.(1.3) can be reformulated as the renowned discrete version of the Schrödinger equation

    Δμ(ξ)+V(ξ)μ(ξ)=λf(ξ,μ(ξ)),in Z. (1.5)

    It is worth mentioning that in [13], Agarwal et al. first employed the variational methods to analyze Eq.(1.5). Here, We give some literature on the study of difference equations using the critical point theory, see [14,15,16].

    In particular, we observe that both the nonlinear terms in [11,12] have the following symmetry condition:

    (S) f(a,ν) is odd in ν.

    Therefore, in this paper, we consider the nonlinear term without condition (S), and study the existence of multiple homoclinic solutions of problem (1.1). For this, let us first recall if the solution ν of Eq.(1.1) satisfies ν(d)0 as |d|, then ν is called a homoclinic solution. Suppose that V(a) and f(a,u(a)) in problem (1.1) satisfy the following assumptions:

    (V) V1 and there is a constant V0(0,infaZV(a)]; (1 is defined in next section)

    (F) |f(a,u)|C(|u|p1+|u|t1) for any aZ and uR, where p<t< and C>0 is a constant.

    Set

    A:=lim infτ0+max|ζ|τaZF(a,ζ(a))τp,B:=lim supτ0+aZF(a,τ(a))τp,θ:=CsV0CbV1,

    where F(a,u)=u0f(a,η)dη and Cs, Cb will appear in next section. Here we give the main conclusion of our paper as follows.

    Theorem 1.1. Suppose that (V) and (F) are satisfied. Furthermore, the following inequality holds: A<θB. Then, for every λ(CbV1pB,CsV0pA), problem (1.1) possesses infinitely many nontrivial homoclinic solutions. In addition, their critical values and their -norms tend to zero.

    The rest of this article is arranged as follows: In Section 2, we introduce some definitions and give some preliminary results. In Section 3, we give the proof of Theorem 1.1. In Section 4, we give an example to demonstrate the main result.

    Here we illustrate some notations used in this paper:

    C, Cs,ω, Cs, Cb and C are diverse positive constants.

    denotes the embedding.

    denotes the strong convergence.

    First we give some basic definitions.

    Let 1ω, we give the definition of the space (ω,ω) as follows:

    ω:={{μ:ZR|aZ|μ(a)|ω<},if1ω<;{μ:ZR|supaZ|μ(a)|<},ifω=;
    μω:={(aZ|μ(a)|ω)1/ω,if1ω<;supaZ|μ(a)|,ifω=.

    Through the corresponding conclusions in [17], we know that ω is a Banach space. Moreover, ω1ω2 and μω2μω1 if 1ω1ω2.

    Next, we give the variational framework and some lemmas of this paper.

    The space (Q,Q) is defined by

    Q={σ:ZR|aZbZ|σ(a)σ(b)|pKs,p(ab)+dZV(d)|σ(d)|p<};
    σpQ=[σ]ps,p+dZV(d)|σ(d)|p=aZbZ|σ(a)σ(b)|pKs,p(ab)+dZV(d)|σ(d)|p.

    Lemma 2.1. (see [10, Lemma 2.1]) If ξω, then [ξ]s,ωCs,ωξω<.

    Lemma 2.2. (see [11, Lemma 2.2]) Under the hypothesis (V), (Q,Q) is a reflexive Banach space, and

    σ:=(aZV(a)|σ(a)|p)1/p.

    is an equivalent norm of Q.

    Through Lemma 2.2, we obtain that there exist 0CsCb such that

    CsμpμpQCbμp. (2.1)

    Lemma 2.3. Under the hypothesis (V), Qr is continuous for all pr.

    Proof. Using the above conclusions and (V), we can deduce that

    σrσp=(aZ|σ(a)|p)1pV1p0(aZV(a)|σ(a)|p)1p,σQ.

    As desired.

    Lemma 2.4. (see [10, Lemma 2.4]) If WQ is a compact subset, then for ι>0, a0N such that

    [|a|>a0V(a)|ξ(a)|p]1/p<ι,for eachξW.

    For all uQ, we define

    K(u)=D(u)λE(u)

    where

    D(u)=1paZbZ|u(a)u(b)|pKs,p(ab)+1pdZV(d)|u(d)|p=1pupQ

    and

    E(u)=dZF(d,u(d)).

    Clearly

    infQD(μ)=infQ1pμpQ=D(0)=0. (2.2)

    Lemma 2.5. (see [10, Lemma 2.5]) Under the hypothesis (V), then D(σ)C1(Q,R) with

    D(σ),ξ=aZbZ|σ(a)σ(b)|p2(σ(a)σ(b))(ξ(a)ξ(b))Ks,p(ab)+dZV(d)|σ(d)|p2σ(d)ξ(d),

    for all σ,ξQ.

    Lemma 2.6. (see [12, Lemma 2.6]) Under the hypotheses (V) and (F), then E(σ)C1(Q,R) with

    E(σ),ξ=dZf(d,σ(d))ξ(d)

    for all σ,ξQ.

    Combining Lemma 2.5 and Lemma 2.6, we know that K(σ)C1(Q,R).

    Lemma 2.7. Under the hypotheses (V) and (F), then for λ>0, every critical point of K is a homoclinic solution of problem (1.1).

    Proof. Assume σ be a critical point of K, we get for ξQ

    aZbZ|σ(a)σ(b)|p2(σ(a)σ(b))(ξ(a)ξ(b))Ks,p(ab)+aZV(a)|σ(a)|p2σ(a)ξ(a)=λaZf(a,σ(a))ξ(a). (2.3)

    For each aZ, we define edQ as follows:

    ed(a):={0,ifad;1,ifa=d.

    Taking ξ=ed in (2.3), we have

    2bZ,ba|u(a)u(b)|p2(u(a)u(b))Ks,p(ab)+V(a)|u(a)|p2u(a)=λf(a,σ(a)).

    So σ is a solution of problem (1.1). Moreover, by Lemma 2.3 and σQ, we know σ(a)0 as |a|. Thus, σ is a homoclinic solution of problem (1.1).

    In this section, we shall use the following Thoerem 3.1 to prove our main result. In fact, this theorem is a special version of Ricceri's variational principle [18, Lemma 2.5].

    Theorem 3.1. (see [19, Lemma 2.1]) Let Q be a reflexive Banach space, K(μ):=D(μ)+λE(μ) for each μQ, where D,EC1(Q,R), D is coercive, and λ is a real positive parameter. For every γ>infQD(μ), let

    η(γ):=infμD1((,γ))(supνD1((,γ))E(ν))E(μ)γD(μ),

    and

    ρ:=lim infγ(infQD(μ))+η(γ)

    If ρ<+, then for every λ(0,1ρ), the following conclusions holds only one:

    (a) there exists a global minimum of D which is a local minimum of K.

    (b) there exists a sequence {μm} of pairwise distinct critical points (local minima) of K, with limmD(μm)=infQD(μ), which converges to a global minimum of D.

    Remark 3.1. Obviously, ρ0. In addition, when ρ=0, we think that 1ρ=+.

    Proof of Theorem 1.1. Let us recall

    A=lim infτ0+max|ζ|τaZF(a,ζ(a))τp,B=lim supτ0+aZF(a,τ(a))τp,θ=CsV0CbV1,

    where F(a,u)=u0f(a,ω)dω. Fix λ(CbV1pB,CsV0pA) and set K,D,E as in Section 2. By Lemma 2.2, Lemma 2.5 and Lemma 2.6, we know Q be a reflexive Banach space and D,EC1(Q,R). Because of

    D(μ)=1paZbZ|μ(a)μ(b)|pKs,p(ab)+1pdZV(d)|μ(d)|p=1pμpQ+

    as μQ+, i.e. D is coercive. Now, we show that ρ<+. For this purpose, let {δn} be a positive sequence such that limnδn=0 and

    limnmax|ζ|δnaZF(a,ζ(a))δpn=A.

    Put

    γn:=CsV0pδpn,

    for all nN. Clearly, limnγn=0. For n>0 is big enough, by Lemma 2.2 and (2.1), we can derive that

    D1((,γn)){νQ:|ν(d)|δn,dZ}. (3.1)

    Since D(0)=E(0)=0, for each n large enough, by (3.1), we get

    η(γn)=infμD1((,γn))(supνD1((,γn))aZF(a,ν(a)))E(μ)γnD(μ)(supνD1((,γn))aZF(a,ν(a)))E(0)γnD(0)=supνD1((,γn))aZF(a,ν(a))γnmax|w|δnaZF(a,w(a))γn=pmax|w|δnaZF(a,w(a))CsV0δpn.

    Therefore, by (2.2), we acquire that

    ρ=lim infγ(infQD(μ))+η(γ)=lim infγn0+η(γn)limnη(γn)limnpmax|w|δnaZF(a,w(a))CsV0δpn=pACsV0. (3.2)

    From (3.2), we get

    λ(CbV1pB,CsV0pA)(0,1ρ).

    Next, we verify that 0 is not a local minimum of K. First, suppose that B=+. Choosing M such that M>CbV1pλ and let {hn} be a sequence of positive numbers, with limnhn=0, there exists n1N such that for all nn1

    aZF(a,hn)>Mhpn. (3.3)

    Therefore, let {ln} be a sequence in Q defined by

    ln(a):=hn,for allaZ.

    It is easy to infer that ln(a)Q0 as n. By (V), (2.1) and (3.3), we obtain

    K(ln)=D(ln)λE(ln)=1plnpQλaZF(a,ln)=1plnpQλaZF(a,hn)CbplnpλaZF(a,hn)=CbpaZV(a)|ln(a)|pλaZF(a,hn)=Cbp(aZV(a))|hn|pλaZF(a,hn)<CbpV1hpnλMhpn=(CbpV1λM)hpn.

    So, K(ln)<0=K(0) for each nn1 big enough. Next, suppose that B<+. Since λ>CbV1pB, there exists ε>0 such that ε<BCbV1pλ. Hence, also choosing {hn} be a sequence of positive numbers, with limnhn=0, there is n2N such that for all nn2

    aZF(a,hn)>(Bε)hpn. (3.4)

    Arguing as before and by choosing {ln} in Q as above, we get

    K(ln)=D(ln)λE(ln)=1plnpQλaZF(a,ln)=1plnpQλaZF(a,hn)CbplnpλaZF(a,hn)=CbpaZV(a)|ln(a)|pλaZF(a,hn)=Cbp(aZV(a))|hn|pλaZF(a,hn)<CbpV1hpnλ(Bε)hpn=(CbpV1λ(Bε))hpn.

    So, K(ln)<0=K(0) for each nn2 big enough. In general, 0 is not a local minimum of K. By Theorem 3.1, (a) is not valid, then we have a sequence {μn}Q of critical points of K such that

    limnD(μn)=limn1pμnQ=infQD(μ)=0

    and

    limnK(μn)=infQD(μ)=0.

    By Lemma 2.3, we gain

    μnCμnQ0

    as n. By Lemma 2.7, the problem (1.1) admits infinitely many nontrivial homoclinic solutions. In addition, their critical values and their -norms tend to zero. This completes the proof.

    Here, we give an example of a nonlinear term which can apply Theorem 1.1.

    Example 4.1. We define

    Ψ(n):=1333n,fornN+;
    Φ(n):=1333n1,fornN+;
    χ(n):=13(p+1)33n3,fornN+.

    Obviously, we know that Φ(n+1)<Ψ(n)<Φ(n) for all nN+ and limnΨ(n)=limnΦ(n)=0. Set

    f(a,u)=0,aZN+.

    And for each aN+, let f(a,) is a nonnegative continuous function such that

    f(a,u)=0,uR(Ψ(a),Φ(a))andΦ(a)Ψ(a)f(a,η)dη=χ(a).

    There are many nonlinear terms that satisfy the above conditions. Here we give one of them as an example.

    f(a,u)=nN+χ(n)2((u+Φ(n)+Ψ(n)2)2Φ2(n)Ψ2(n))e{n}×[Ψ(n),Φ(n)](a,u)

    where eM×N is the indicator function on M×N. Then

    A=lim infτ0+max|ζ|τaZF(a,ζ(a))τplimnmax|ζ|Ψ(n)aZF(a,ζ(a))Ψp(n)=limna=n+1F(a,ζ(a))Ψp(n)=limna=n+1χ(a)Ψp(n)limn3χ(n+1)Ψp(n)=0

    and

    B=lim supτ0+aZF(a,ζ(a))τplimnaZF(a,ζ(a))Φp(n)limnF(n,ζ(n))Φp(n)limnχ(n)Φp(n)=+.

    Now it is easy to see that all the assumptions of Theorem 1.1 are satisfied, hence the corresponding conclusion can be delivered by Theorem 1.1.

    B. Zhang was supported by the National Natural Science Foundation of China (No. 12171152), the Shandong Provincial Natural Science Foundation, PR China (No. ZR2023MA090) and the Cultivation Project of Young and Innovative Talents in Universities of Shandong Province.

    The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.



    [1] J. R. Wolpaw, N. Birbaumer, W. J. Heetderks, D. J. McFarland, P. H. Peckham, G. Schalk, et al., Brain-computer interface technology: A review of the first international meeting, IEEE Trans. Neural Syst. Rehabil. Eng., 8 (2000), 164–173. https://doi.org/10.1109/TRE.2000.847807 doi: 10.1109/TRE.2000.847807
    [2] J. R. Wolpaw, N. Birbaumer, D. J. McFarland, G. Pfurtscheller, T. M. Vaughan, Brain–computer interfaces for communication and control, Clin. Neurophysiol., 113 (2002), 767–791. https://doi.org/10.1016/S1388-2457(02)00057-3 doi: 10.1016/S1388-2457(02)00057-3
    [3] V. Mihajlović, B. Grundlehner, R. Vullers, J. Penders, Wearable, wireless EEG solutions in daily life applications: What are we missing, IEEE J. Biomed. Health Inf., 19 (2015), 6–21. https://doi.org/10.1109/JBHI.2014.2328317 doi: 10.1109/JBHI.2014.2328317
    [4] Y. Jiao, Y. Zhang, X. Chen, E. Yin, J. Jin, X. Wang, et al., Sparse group representation model for motor imagery EEG classification, IEEE J. Biomed. Health Inf., 23 (2018), 631–641. https://doi.org/10.1109/JBHI.2018.2832538 doi: 10.1109/JBHI.2018.2832538
    [5] T. D. Pham, Classification of motor-imagery tasks using a large EEG dataset by fusing classifiers learning on wavelet-scattering features, IEEE Trans. Neural Syst. Rehabil. Eng., 31 (2023), 1097–1107. https://doi.org/10.1109/TNSRE.2023.3241241 doi: 10.1109/TNSRE.2023.3241241
    [6] W. Y. Hsu, Y. W. Cheng, EEG-Channel-Temporal-Spectral-Attention correlation for motor imagery EEG classification, IEEE Trans. Neural Syst. Rehabil. Eng., 31 (2023), 1659–1669. https://doi.org/10.1109/TNSRE.2023.3255233 doi: 10.1109/TNSRE.2023.3255233
    [7] C. Liu, J. Jin, I Daly, S Li, H. Sun, Y. Huang, et al., SincNet-based hybrid neural network for motor imagery EEG decoding, IEEE Trans. Neural Syst. Rehabil. Eng., 30 (2022), 540–549. https://doi.org/10.1109/TNSRE.2022.3156076 doi: 10.1109/TNSRE.2022.3156076
    [8] X. Yin, M. Meng, Q. She, Y. Gao, Z. Luo, Optimal channel-based sparse time-frequency blocks common spatial pattern feature extraction method for motor imagery classification, Math. Biosci. Eng., 18 (2021), 4247–4263. https://doi.org/10.3934/mbe.2021213 doi: 10.3934/mbe.2021213
    [9] S. Vaid, P. Singh, C. Kaur, EEG signal analysis for BCI interface: A review, in Fifth International Conference on Advanced Computing & Communication Technologies, (2015), 143–147. https://doi.org/10.1109/ACCT.2015.72
    [10] Y. Li, X. D. Wang, M. L. Luo, K. Li, X. F. Yang, Q. Guo, Epileptic seizure classification of EEGs using time–frequency analysis based multiscale radial basis functions, IEEE J. Biomed. Health Inf., 22 (2017), 386–397. https://doi.org/10.1109/JBHI.2017.2654479 doi: 10.1109/JBHI.2017.2654479
    [11] J. W. Li, S. Barma, P. U. Mak, F. Chen, C. Li, M. Li, et al., Single-channel selection for EEG-based emotion recognition using brain rhythm sequencing, IEEE J. Biomed. Health Inf., 26 (2022), 2493–2503. https://doi.org/10.1109/JBHI.2022.3148109 doi: 10.1109/JBHI.2022.3148109
    [12] F. Lotte, C. Guan, Regularizing common spatial patterns to improve BCI designs: Unified theory and new algorithms, IEEE Trans. Biomed. Eng., 58 (2010), 355–362. https://doi.org/10.1109/TBME.2010.2082539 doi: 10.1109/TBME.2010.2082539
    [13] H. Ramoser, J. Muller-Gerking, G. Pfurtscheller, Optimal spatial filtering of single trial EEG during imagined hand movement, IEEE Trans. Neural Syst. Rehabil. Eng., 8 (2000), 441–446. https://doi.org/10.1109/86.895946 doi: 10.1109/86.895946
    [14] P. Herman, G. Prasad, T. M. McGinnity, D. Coyle, Comparative analysis of spectral approaches to feature extraction for EEG-Based motor imagery classification, IEEE Trans. Neural Syst. Rehabil. Eng., 16 (2008), 317–326. https://doi.org/10.1109/TNSRE.2008.926694 doi: 10.1109/TNSRE.2008.926694
    [15] B. Orset, K. Lee, R. Chavarriaga, J. Millán, User adaptation to closed-loop decoding of motor imagery termination, IEEE Trans. Biomed. Eng., 68 (2020), 3–10. https://doi.org/10.1109/TBME.2020.3001981 doi: 10.1109/TBME.2020.3001981
    [16] Y. Zhang, C. S. Nam, G. Zhou, J. Jin, X. Wang, A. Cichocki, Temporally constrained sparse group spatial patterns for motor imagery BCI, IEEE Trans. Cyber., 49 (2018), 3322–3332. https://doi.org/10.1109/TCYB.2018.2841847 doi: 10.1109/TCYB.2018.2841847
    [17] M. Lee, Y. H. Kim, S. W. Lee, Motor impairment in stroke patients is associated with network properties during consecutive motor imagery, IEEE Trans. Biomed. Eng., 69 (2022), 2604–2615. https://doi.org/10.1109/TBME.2022.3151742 doi: 10.1109/TBME.2022.3151742
    [18] Y. Y. Miao, J. Jin, L. Daly, C. Zuo, X. Wang, A. Cichocki, et al., Learning common time-frequency-spatial patterns for motor imagery classification, IEEE Trans. Neural Syst. Rehabil. Eng., 29 (2021), 699–707. https://doi.org/10.1109/TNSRE.2021.3071140 doi: 10.1109/TNSRE.2021.3071140
    [19] D. Hong, L. Gao, J. Yao, B. Zhang, A. Plaza, J. Chanussot, Graph convolutional networks for hyperspectral image classification, IEEE Trans. Geosci. Remote Sens., 59 (2021), 5966–5978. https://doi.org/10.1109/TGRS.2020.3015157 doi: 10.1109/TGRS.2020.3015157
    [20] C. Li, B. Zhang, D. Hong, J. Yao, J. Chanussot, LRR-Net: An interpretable deep unfolding network for hyperspectral anomaly detection, IEEE Trans. Geosci. Remote Sens., 61 (2023), 1–12. https://doi.org/10.1109/TGRS.2023.3279834 doi: 10.1109/TGRS.2023.3279834
    [21] J. Yao, B. Zhang, C. Li, D. Hong, J. Chanussot, Extended Vision Transformer (ExViT) for land use and land cover classification: A multimodal deep learning framework, IEEE Trans. Geosci. Remote Sens., 61 (2023), 1–15. https://doi.org/10.1109/TGRS.2023.3284671 doi: 10.1109/TGRS.2023.3284671
    [22] D. Hong, B. Zhang, H. Li, Y. Li, J. Yao, C. Li, et al., Cross-city matters: A multimodal remote sensing benchmark dataset for cross-city semantic segmentation using high-resolution domain adaptation networks, Remote Sens. Environ., 299 (2023). https://doi.org/10.1016/j.rse.2023.113856 doi: 10.1016/j.rse.2023.113856
    [23] P. Zhang, X. Wang, W. Zhang, J. Chen, Learning spatial–spectral–temporal EEG features with recurrent 3D convolutional neural networks for cross-task mental workload assessment, IEEE Trans. Neural Syst. Rehabil. Eng., 27 (2019), 31–42. https://doi.org/10.1109/TNSRE.2018.2884641 doi: 10.1109/TNSRE.2018.2884641
    [24] S. Sakhavi, C. Guan, S. Yan, Learning temporal information for brain-computer interface using convolutional neural networks, IEEE Trans. Neural Networks Learn. Syst., 29 (2018), 5619–5629. https://doi.org/10.1109/TNNLS.2018.2789927 doi: 10.1109/TNNLS.2018.2789927
    [25] B. E. Olivas-Padilla, M. I. Chacon-Murguia, Classification of multiple motor imagery using deep convolutional neural networks and spatial filters, Appl. Soft Comput., 75 (2019), 461–472. https://doi.org/10.1016/j.asoc.2018.11.031 doi: 10.1016/j.asoc.2018.11.031
    [26] X. Ma, S. Qiu, H. He, Time-distributed attention network for EEG-based motor imagery decoding from the same limb, IEEE Trans. Neural Syst. Rehabil. Eng., 30 (2022), 496–508. https://doi.org/10.1109/TNSRE.2022.3154369 doi: 10.1109/TNSRE.2022.3154369
    [27] R. Zhang, N. L. Zhang, C. Chen, D. Y. Lv, G. Liu, F. Peng, et al., Motor imagery EEG classification with self-attention-based convolutional neural network, in 7th International Conference on Intelligent Informatics and Biomedical Science (ICⅡBMS), (2022), 195–199. https://doi.org/10.1109/ICⅡBMS55689.2022.9971698
    [28] J. Zheng, M. Liang, S. Sinha, L. Ge, W. Yu, A. Ekstrom, et al., Time-frequency analysis of scalp EEG with Hilbert-Huang transform and deep learning, IEEE J. Biomed. Health. Inf., 26 (2022), 1549–1559. https://doi.org/10.1109/JBHI.2021.3110267 doi: 10.1109/JBHI.2021.3110267
    [29] H. Fang, J. Jin, I. Daly, X. Wang, Feature extraction method based on filter banks and Riemannian tangent space in motor-imagery BCI, IEEE J. Biomed. Health. Inf., 26 (2022), 2504–2514. https://doi.org/10.1109/JBHI.2022.3146274 doi: 10.1109/JBHI.2022.3146274
    [30] F. Lotte, L. Bougrain, M. Clerc, Electroencephalography (EEG)-based brain-computer interfaces, in Wiley Encyclopedia of Electrical and Electronics Engineering, Wiley, (2015). https://doi.org/10.1002/047134608X.W8278
    [31] G. Pfurtscheller, C. Neuper, D. Flotzinger, M. Pregenzer, EEG-based discrimination between imagination of right and left hand movement, Electroencephalogr. Clin. Neurophysiol., 103 (1997), 642–651. https://doi.org/10.1016/S0013-4694(97)00080-1 doi: 10.1016/S0013-4694(97)00080-1
    [32] R. Chai, S. H. Ling, G. P. Hunter, Y. Tran, H. T. Nguyen, Brain–computer interface classifier for wheelchair commands using neural network with fuzzy particle swarm optimization, IEEE J. Biomed. Health. Inf., 18 (2014), 1614–1624. https://doi.org/10.1109/JBHI.2013.2295006 doi: 10.1109/JBHI.2013.2295006
    [33] K. K. Ang, Z. Y. Chin, H. Zhang, C. Guan, Filter bank common spatial pattern (FBCSP) in brain-computer interface, in 2008 IEEE International Joint Conference on Neural Networks, (2008), 2390–2397. https://doi.org/10.1109/IJCNN.2008.4634130
    [34] K. P. Thomas, C. Guan, C. T. Lau, A. P. Vinod, K. K. Ang, A new discriminative common spatial pattern method for motor imagery brain–computer interfaces, IEEE Trans. Biomed. Eng., 56 (2009), 2730–2733. https://doi.org/10.1109/TBME.2009.2026181 doi: 10.1109/TBME.2009.2026181
    [35] D. Hong, J. Yao, C. Li, D. Meng, N. Yokoya, J. Chanussot, Decoupled-and-coupled networks: Self-supervised hyperspectral image super-resolution with subpixel fusion, IEEE Trans. Geosci. Remote Sens., 61 (2023), 1–12. https://doi.org/10.1109/TGRS.2023.3324497 doi: 10.1109/TGRS.2023.3324497
    [36] Y. Yuan, G. Xun, K. Jia, A. Zhang, A multi-view deep learning framework for EEG seizure detection, IEEE J. Biomed. Health Inf., 23 (2019), 83–94. https://doi.org/10.1109/JBHI.2018.2871678 doi: 10.1109/JBHI.2018.2871678
    [37] D. Zhang, K. Chen, D. Jian, L. Yao, Motor imagery classification via temporal attention cues of graph embedded EEG signals, IEEE J. Biomed. Health Inf., 24 (2020), 2570–2579. https://doi.org/10.1109/JBHI.2020.2967128 doi: 10.1109/JBHI.2020.2967128
    [38] W. Wu, X. Gao, B. Hong, S. Gao, Classifying single-trial EEG during motor imagery by iterative spatio-spectral patterns learning (ISSPL), IEEE Trans. Biomed. Eng., 55 (2008), 1733–1743. https://doi.org/10.1109/TBME.2008.919125 doi: 10.1109/TBME.2008.919125
    [39] F. Qi, Y. Li, W. Wu, RSTFC: A novel algorithm for spatio-temporal filtering and classification of single-trial EEG, IEEE Trans. Neural Networks Learn. Syst., 26 (2015), 3070–3082. https://doi.org/10.1109/TNNLS.2015.2402694 doi: 10.1109/TNNLS.2015.2402694
    [40] D. Li, J. Xu, J. Wang, X. Fang, Y. Ji, A multi-scale fusion convolutional neural network based on attention mechanism for the visualization analysis of EEG signals decoding, IEEE Trans. Neural Syst. Rehabil. Eng., 28 (2020), 2615–2626. https://doi.org/10.1109/TNSRE.2020.3037326 doi: 10.1109/TNSRE.2020.3037326
    [41] K. He, X. Zhang, S. Ren, J. Sun, Deep residual learning for image recognition, arXiv preprint, (2015), arXiv: 1512.03385. https://doi.org/10.48550/arXiv.1512.03385
    [42] D. Arthur, S. Vassilvitskii, k-means++: The advantages of careful seeding, in Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, (2007), 1027–1035.
    [43] K. K. Ang, Z. Y. Chin, C. Wang, C. Guan, H. Zhang, Filter bank common spatial pattern algorithm on BCI competition Ⅳ Datasets 2a and 2b, Front. Neurosci., 6 (2012), 39. https://doi.org/10.3389/fnins.2012.00039 doi: 10.3389/fnins.2012.00039
    [44] R. T. Schirrmeister, J. T. Sprongenberg, L. D. J. Fiederer, M. Glasstetter, K. Eggensperger, M. Tangermann, et al., Deep learning with convolutional neural networks for EEG decoding and visualization, Hum. Brain Mapp., 38 (2017), 5391–542. https://doi.org/10.1002/hbm.23730 doi: 10.1002/hbm.23730
    [45] X. Zhao, H. Zhang, G. Zhu, F. You, S. Kuang, L. Sun, A multi-branch 3D convolutional neural network for EEG-based motor imagery classification, IEEE Trans. Neural Syst. Rehabil. Eng., 27 (2019), 2164–2177. https://doi.org/10.1109/TNSRE.2019.2938295 doi: 10.1109/TNSRE.2019.2938295
    [46] R. R. Selvaraju, M. Cogswell, A. Das, R. Vedantam, D. Parikh, D. Batra, Grad-CAM: Visual explanations from deep networks via gradient-based localization, in 2017 IEEE International Conference on Computer Vision (ICCV), (2017), 618–626. https://doi.org/10.1109/ICCV.2017.74
    [47] D. Hong, N. Yokoya, J. Chanussot, X. Zhu, An augmented linear mixing model to address spectral variability for hyperspectral unmixing, IEEE Trans. Image Process., 28 (2019), 1923–1938. https://doi.org/10.1109/TIP.2018.2878958 doi: 10.1109/TIP.2018.2878958
    [48] R. K. Meleppat, C. R. Fortenbach, Y. Jian, E. S. Martinez, K. Wagner, B. S. Modjtahedi, et al., In vivo imaging of retinal and choroidal morphology and vascular plexuses of vertebrates using swept-source optical coherence tomography, Transl. Vision Sci. Technol., 11 (2022), 11. https://doi.org/10.1167/tvst.11.8.11 doi: 10.1167/tvst.11.8.11
    [49] K. M. Ratheesh, L. K. Seah, V. M. Murukeshan, Spectral phase-based automatic calibration scheme for swept source-based optical coherence tomography systems, Phys. Med. Biol., 61 (2016), 7652–7663. https://doi.org/10.1088/0031-9155/61/21/7652 doi: 10.1088/0031-9155/61/21/7652
    [50] R. K. Meleppat, E. B. Miller, S. K. Manna, P. Zhang, E. N. Pugh, R. J. Zawadzki, Multiscale hessian filtering for enhancement of OCT angiography images, in Ophthalmic Technologies XXIX, (2019), 64–70. https://doi.org/10.1117/12.2511044
    [51] R. K. Meleppat, P. Prabhathan, S. L. Keey, M. V. Matham, Plasmon resonant silica-coated silver nanoplates as contrast agents for optical coherence tomography, J. Biomed. Nanotechnol., 12 (2016), 1929–1937. https://doi.org/10.1166/jbn.2016.2297 doi: 10.1166/jbn.2016.2297
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