222
6 Deep Learning and RFID System Physical Anti-Collision
By Eqs. (6.20) and (6.21), we can conclude that the image priori can be replaced
by the denoiser priori. This excellent feature has the following advantages. Firstly,
the various image inverse problems can be solved by using different gray or color
denoiser. Secondly, when solving Eq. (6.16), the explicit image priori (•) may be
unknown. Thirdly, several different image prior denoisers can be combined to solve
a specific problem.
6.4.3 Method from Multi-level WPT to MWCNN
In this chapter, we use multi-level wavelet convolution neural network to train the
denoiser priori. First, we introduce multi-level wavelet packet transform (WPT). Then
we present our MWCNN motivated by WPT, and describe its network architecture.
In the case of the two-dimensional discrete wavelet transform, image x is convoluted with four sub-filters f LL , f LH , f HL, and f HH , and the convolution results are
sampled down to obtain the processed images x 1 , x 2 , x 3, and x 4 . For example, x 1 is
defined as ( f L L ⊗ x) ↓ 2 . Because of the biorthogonal property of wavelet transform,
the original image can be reconstructed precisely by inverse transform, that is, x =
IWT(x 1 , x 2 , x 3 , x 4 ).
In the multi-level wavelet packet transform, the sub-band images x 1 , x 2 , x 3, and
x 4 of two-dimensional decomposition are further decomposed. Taking two-stage
wavelet packet transform as an example, the upper decomposition sub-band image
x i (i = 1,2,3or4) is further decomposed as x i,1 , x i,2 , x i,3 , and x i,4 . For the third or
higher level wavelet packet transform, the situation is the same. In fact, WPT is
a linear special case of FCN. In the decomposition stage, each sub-band image is
convoluted and down-sampled successively. In the reconstruction stage, the sub-band
image is first sampled and then deconvoluted. Finally, the original image x can be
accurately reconstructed by inverse WPT.
In image inverse problems, such as image denoising, restoration, and reconstruction, some nonlinear operations, such as normalization and quantization, are usually
added to deal with the results of the wavelet transform. These operations can be
regarded as some kind of nonlinearity designed for a specific inverse problem. Specifically, we plan to add a CNN module between any two levels of DWT to extend WPT
to multi-level wavelet CNN. In this way, the self-contained image of each level of
wavelet transform can be used as the input of the CNN module, so as to make
full use of the excellent time–frequency characteristics of DWT and the powerful
nonlinear feature extraction ability of CNN. Compared with the traditional CNN,
the time–frequency characteristics of DWT are more conducive to the preservation
of high-frequency information such as image texture details.
6 Deep Learning and RFID System Physical Anti-Collision
By Eqs. (6.20) and (6.21), we can conclude that the image priori can be replaced
by the denoiser priori. This excellent feature has the following advantages. Firstly,
the various image inverse problems can be solved by using different gray or color
denoiser. Secondly, when solving Eq. (6.16), the explicit image priori (•) may be
unknown. Thirdly, several different image prior denoisers can be combined to solve
a specific problem.
6.4.3 Method from Multi-level WPT to MWCNN
In this chapter, we use multi-level wavelet convolution neural network to train the
denoiser priori. First, we introduce multi-level wavelet packet transform (WPT). Then
we present our MWCNN motivated by WPT, and describe its network architecture.
In the case of the two-dimensional discrete wavelet transform, image x is convoluted with four sub-filters f LL , f LH , f HL, and f HH , and the convolution results are
sampled down to obtain the processed images x 1 , x 2 , x 3, and x 4 . For example, x 1 is
defined as ( f L L ⊗ x) ↓ 2 . Because of the biorthogonal property of wavelet transform,
the original image can be reconstructed precisely by inverse transform, that is, x =
IWT(x 1 , x 2 , x 3 , x 4 ).
In the multi-level wavelet packet transform, the sub-band images x 1 , x 2 , x 3, and
x 4 of two-dimensional decomposition are further decomposed. Taking two-stage
wavelet packet transform as an example, the upper decomposition sub-band image
x i (i = 1,2,3or4) is further decomposed as x i,1 , x i,2 , x i,3 , and x i,4 . For the third or
higher level wavelet packet transform, the situation is the same. In fact, WPT is
a linear special case of FCN. In the decomposition stage, each sub-band image is
convoluted and down-sampled successively. In the reconstruction stage, the sub-band
image is first sampled and then deconvoluted. Finally, the original image x can be
accurately reconstructed by inverse WPT.
In image inverse problems, such as image denoising, restoration, and reconstruction, some nonlinear operations, such as normalization and quantization, are usually
added to deal with the results of the wavelet transform. These operations can be
regarded as some kind of nonlinearity designed for a specific inverse problem. Specifically, we plan to add a CNN module between any two levels of DWT to extend WPT
to multi-level wavelet CNN. In this way, the self-contained image of each level of
wavelet transform can be used as the input of the CNN module, so as to make
full use of the excellent time–frequency characteristics of DWT and the powerful
nonlinear feature extraction ability of CNN. Compared with the traditional CNN,
the time–frequency characteristics of DWT are more conducive to the preservation
of high-frequency information such as image texture details.