О СВОЙСТВАХ СОБСТВЕННЫХ ВЕКТОРОВ СУБПОЛОСНЫХ МАТРИЦ

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  • 621.397

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    e-mail: chernomorets@bsu.edu.ru

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    1, 2, 1, 2 .

  • .. , .. .

    123

    , -.

    F(u,v), Z(u,v) - =(fik), i=1,2,,M, k=1,2,,N, Y=(yik), i=1,2,,M, k=1,2,,N, ( , ):

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    kjvijuikM

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    kjvijuikM

    i

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    - . . , - (2) , =0,5.

    - Y , - . , Z(u,v) Y - F(u,v) , . (2)

    min),(),(),(),(),(

    2

    ),(

    2 vuvu

    dudvvuZdudvvuZvuFZFS , (3)

    |Z(u,v)| |F(u,v)| , .

    [3] , Y , - (3), , -

    BAY T , (4) A=(ai1i2), i1,i2=1,2,,M, B=(bk1k2), k1,k2=1,2,,N, [4], - (1), -

    ,,

    ,,)(

    )()(

    2112

    2121

    211212

    21

    ii

    iiii

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    a ii

    .,

    ,,)(

    )()(

    2112

    2121

    211212

    21

    kk

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    Y, - ,

    knimik

    N

    k

    M

    imn bafy

    11. (5)

    , (4), O(M2N2). -

  • 7 (62) 2009

    124

    .

    -

    [5] , -

    M

    iiAiiAiAiii

    a

    aaaqqa

    12121

    ,

    N

    kkBkkBkBkkk

    b

    bbbqqb

    12121

    ,

    AMAA ,...,, 21 BNBB ,...,, 21 ,

    AMAA qqq ,...,, 21 BNBB qqq

    ,...,, 21 . , , ..

    AMAA ...21 , BMBB ...21 . (5) :

    bbaaba

    ba

    BnkBkkikAii

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    imn qqfqqy )(

    1111

    . (6)

    [6] TAAA QLQA , (7) TBBB QLQB , (8)

    QA QB A B , ..

    ),...,,( 21 AMAAA qqqQ , ),...,,( 21 BNBBB qqqQ

    , LA LB , , ..

    ),...,,( 21 AMAAA diagL , ),...,,( 21 BMBBB diagL . (7), (8) (4), -

    TBBB

    TAAA QLQQLQY . (9)

    Q , - .

    r1,r2, r1=1,2,, Ra, r2=1,2,, Rb, ( - Ra Rb - ).

    - : 16, 128128 . . 1, 2 , . - , 1- 2- , - .

    , . 1, 2 . 1, , , , , .

  • .. , .. .

    125

    . 1. , 1- :

    ,

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    , ( - 16, 128128 ).

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    Ja Jb .

  • 7 (62) 2009

    126

    1

    12 , N=128

    -

    -

    1 2 3 4 5 6 7 8 9 10 11 12

    1 1 1 1 1 0.999 0.993 0.937 0.699 0.299 0.064 0.008 0.001 2 1 1 0.998 0.997 0.964 0.958 0.729 0.72 0.276 0.268 0.045 0.037 3 1 1 0.998 0.998 0.961 0.959 0.724 0.721 0.275 0.272 0.043 0.041 4 1 1 0.998 0.998 0.96 0.959 0.723 0.722 0.275 0.274 0.043 0.042 5 1 1 0.998 0.998 0.96 0.959 0.723 0.722 0.275 0.274 0.043 0.042 6 1 1 0.998 0.998 0.96 0.959 0.722 0.722 0.275 0.274 0.043 0.043 7 1 1 0.998 0.998 0.96 0.959 0.722 0.722 0.275 0.274 0.043 0.043 8 1 1 0.998 0.998 0.96 0.96 0.722 0.722 0.274 0.274 0.043 0.043

    , (7) (8), -

    A B Ra Rb -

    TAAA QLQA 111 ,

    TBBB QLQB 111 ,

    ),...,,( 211 aAJAAA qqqQ

    , ),...,,( 211 bBJBBB qqqQ ,

    ),...,,( 211 aAJAAA diagL , ),...,,( 211 bBJBBB diagL . -

    TBBB

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    - (10)

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  • .. , .. .

    127

    -, R. NN, N=256, . R () Y0 YE, NxN. 1,

    N

    i

    N

    kik

    N

    i

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    20

    1 1

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    )( . (12)

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    R

    i

    R

    kikYEikY

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    20

    1 1

    20

    2

    )( . (13)

    1 2, - R, . 2.

    2

    Y0 YE

    R 2 4 8 16 32 64

    - 1

    0.0021 0.0025 0.0023 0.0017 0.0012 0.00071

    - 2

    3.86e-6 8.37e-6 4.2e-6 2.54e-5 1.35e-5 1.19e-5

    - .

    - - .

    1. [] / .. -. .: , 2003. 784 .

    2. . [] / . , . . .: , 2006. 1072 .

    3. , .. - [] / .. , .. // . . , 2008. . 1. . 118-131.

    4. , .. [] / .. , - , 2007. 160 .

  • 7 (62) 2009

    128

    5. , .. [] / .. , .. , .. // - . . , 2007. . 4. . 115-123.

    6. , .. [] / .. , .. , .. // . , 2006. 174. . 163-170.

    ABOUT PROPERTIES OF SUBBAND MATRICES EIGENVECTORS A.A. CHERNOMORETS E.I. PROKHORENKO V.A. GOLOSCHAPOVA

    Belgorod State University e-mail: chernomorets@bsu.edu.ru

    The properties of subband matrices used in the optimal image fil-

    tration on the basis of frequency representations are described in the work. Results of experimental investigations of efficiency of the opti-mal filtration subject to subbband matrices properties are given

    Key words: subband matrix, image processing, eigenvector,

    filtration

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