a = np.arange(16).reshape(4,4)
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])
b = a[::2,1::2] and at the same time a[1::2,::2]
array([[ 1,  3],
       [ 4, 6],
       [9, 11],
       [12,14]])

a = np.arange(16).reshape(4,4)
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15]])
b = np.zeros((a.shape[0], a.shape[1]/2))
b[::2,:]  = a[::2,1::2]
b[1::2,:] = a[1::2,::2]
>>>> b
array([[  1.,   3.],
   [  4.,   6.],
   [  9.,  11.],
   [ 12.,  14.]])