A

q1 q2

W

Y

1

1 2; ,

K

kk

k k

p p

p Ga q q

α

1

11; ,

KTk

k

T T Tk k k

p p

p N

W w

w w 0 S S

u1 u2

1

1 2; ,

N

nn

n n

p p

p Ga u u

λ1

1

( ) ( )

( ) ( ; , )

N

nn

n n P

p p

p N

A a

a a 0 I

Y=XW+E

Global prior in SPM2:

[TxN] [TxK] [KxN] [TxN]

Laplacian prior:

S L

S I

Figure 1

y

x t

Figure 2

4-1

-1 -1-1

-8-8 -8

-8

2

2 2

21 1

1

1

Figure 3

20

ˆˆ( ) ; ,n n n nq Nw w w Σ

T Tdiag B H α S S H

1,

ˆN

n ni ii i n

r B w

1

Tnn n n n

n n n nn

w Σ b r

Σ A B

1

1

2

; ,

1 1 1

2

2

K

kk

k k k k

TT T

k k k

k

k

k k k

q q

q Ga g h

Trg q

Nh q

g h

α

Σ S S w S Sw

1

2

( ) ( ; , )

1 1

2

2

n n n n

n

n

n

q Ga b c

G

b u

Tc u

1

( ) ( ; , )

( )

n n n n

n n n P

n n n n

q N

a a m V

V C I

m D V

Regression coefficients

Spatial precisions

Observation noise

AR coefficients

( , , , | ) ( | ) ( | ) ( | ) ( | )n n nn

q q q q q

W A λ α Y w Y a Y Y α Y

y

x

y

x

Figure 5

Iteration Number

F

Figure 6

(a) (b)

(c) (d)

Figure 7

1-Specificity

Sen

sitiv

ityFigure 8

Figure 9

(a) (b)

(c) (d)

Figure 10

(a) (b)

(c) (d)

Figure 11

(d)

(a) (b)

(c) (d)

Figure 12

(a) (b)

(c) (d)

Figure 13