By minimizing the energy functional

we can obtain the variational image decomposition which decomposes image into different characteristic components

and can be used for image restoration and reconstruction.An idea of multiscale image restoration and reconstruction in the framework of variation is proposed.Based on this idea

firstly

a single-parameter (BV

G

E

) trituple decomposition model is proposed

and the relationship between the parameter and the scale of each component is studied theoretically.And then

by replacing the parameter with a binary sequence

we achieve a multiscale (BV

G

E

) decomposition which can decompose an image into a

sequence of image structure

texture and noise.The convergence of this multiscale decomposition is proved

and an efficient numerical method based on the duality theory and alternate iteration algorithm is introduced to solve it.At last

the proposed multiscale (BV

G

E

) decomposition is applied for image restoration and reconstruction.Numerical results support the theoretical results and show that the proposed model is efficient for multiscale image restoration and reconstruction

and is superior to some other decomposition models.