创新点
- 在不显著增加复杂度的情况下，显著增加感受野。
- 可以替代传统的卷积模块
- 对分解出的不同频率特征进行独立的卷积处理而且可以捕获频域信息
import pywt
import pywt.data
import torch
from torch import nn
from torch.autograd import Function
import torch.nn.functional as F
def create_wavelet_filter(wave, in_size, out_size, type=torch.float):
w = pywt.Wavelet(wave)
dec_hi = torch.tensor(w.dec_hi[::-1], dtype=type)
dec_lo = torch.tensor(w.dec_lo[::-1], dtype=type)
dec_filters = torch.stack([dec_lo.unsqueeze(0) * dec_lo.unsqueeze(1),
dec_lo.unsqueeze(0) * dec_hi.unsqueeze(1),
dec_hi.unsqueeze(0) * dec_lo.unsqueeze(1),
dec_hi.unsqueeze(0) * dec_hi.unsqueeze(1)], dim=0)
dec_filters = dec_filters[:, None].repeat(in_size, 1, 1, 1)
rec_hi = torch.tensor(w.rec_hi[::-1], dtype=type).flip(dims=[0])
rec_lo = torch.tensor(w.rec_lo[::-1], dtype=type).flip(dims=[0])
rec_filters = torch.stack([rec_lo.unsqueeze(0) * rec_lo.unsqueeze(1),
rec_lo.unsqueeze(0) * rec_hi.unsqueeze(1),
rec_hi.unsqueeze(0) * rec_lo.unsqueeze(1),
rec_hi.unsqueeze(0) * rec_hi.unsqueeze(1)], dim=0)
rec_filters = rec_filters[:, None].repeat(out_size, 1, 1, 1)
return dec_filters, rec_filters
def wavelet_transform(x, filters):
b, c, h, w = x.shape
pad = (filters.shape[2] // 2 - 1, filters.shape[3] // 2 - 1)
x = F.conv2d(x, filters, stride=2, groups=c, padding=pad)
x = x.reshape(b, c, 4, h // 2, w // 2)
return x
def inverse_wavelet_transform(x, filters):
b, c, _, h_half, w_half = x.shape
pad = (filters.shape[2] // 2 - 1, filters.shape[3] // 2 - 1)
x = x.reshape(b, c * 4, h_half, w_half)
x = F.conv_transpose2d(x, filters, stride=2, groups=c, padding=pad)
return x
def wavelet_transform_init(filters):
class WaveletTransform(Function):
@staticmethod
def forward(ctx, input):
with torch.no_grad():
x = wavelet_transform(input, filters)
return x
@staticmethod
def backward(ctx, grad_output):
grad = inverse_wavelet_transform(grad_output, filters)
return grad, None
return WaveletTransform().apply
def inverse_wavelet_transform_init(filters):
class InverseWaveletTransform(Function):
@staticmethod
def forward(ctx, input):
with torch.no_grad():
x = inverse_wavelet_transform(input, filters)
return x
@staticmethod
def backward(ctx, grad_output):
grad = wavelet_transform(grad_output, filters)
return grad, None
return InverseWaveletTransform().apply
class WTConv2d(nn.Module):
def __init__(self, in_channels, out_channels, kernel_size=5, stride=1, bias=True, wt_levels=1, wt_type='db1'):
super(WTConv2d, self).__init__()
assert in_channels == out_channels
self.in_channels = in_channels
self.wt_levels = wt_levels
self.stride = stride
self.dilation = 1
self.wt_filter, self.iwt_filter = create_wavelet_filter(wt_type, in_channels, in_channels, torch.float)
self.wt_filter = nn.Parameter(self.wt_filter, requires_grad=False)
self.iwt_filter = nn.Parameter(self.iwt_filter, requires_grad=False)
self.wt_function = wavelet_transform_init(self.wt_filter)
self.iwt_function = inverse_wavelet_transform_init(self.iwt_filter)
self.base_conv = nn.Conv2d(in_channels, in_channels, kernel_size, padding='same', stride=1, dilation=1,
groups=in_channels, bias=bias)
self.base_scale = _ScaleModule([1, in_channels, 1, 1])
self.wavelet_convs = nn.ModuleList(
[nn.Conv2d(in_channels * 4, in_channels * 4, kernel_size, padding='same', stride=1, dilation=1,
groups=in_channels * 4, bias=False) for _ in range(self.wt_levels)]
)
self.wavelet_scale = nn.ModuleList(
[_ScaleModule([1, in_channels * 4, 1, 1], init_scale=0.1) for _ in range(self.wt_levels)]
)
if self.stride > 1:
self.stride_filter = nn.Parameter(torch.ones(in_channels, 1, 1, 1), requires_grad=False)
self.do_stride = lambda x_in: F.conv2d(x_in, self.stride_filter, bias=None, stride=self.stride,
groups=in_channels)
else:
self.do_stride = None
def forward(self, x):
x_ll_in_levels = []
x_h_in_levels = []
shapes_in_levels = []
curr_x_ll = x
for i in range(self.wt_levels):
curr_shape = curr_x_ll.shape
shapes_in_levels.append(curr_shape)
if (curr_shape[2] % 2 > 0) or (curr_shape[3] % 2 > 0):
curr_pads = (0, curr_shape[3] % 2, 0, curr_shape[2] % 2)
curr_x_ll = F.pad(curr_x_ll, curr_pads)
curr_x = self.wt_function(curr_x_ll)
curr_x_ll = curr_x[:, :, 0, :, :]
shape_x = curr_x.shape
curr_x_tag = curr_x.reshape(shape_x[0], shape_x[1] * 4, shape_x[3], shape_x[4])
curr_x_tag = self.wavelet_scale[i](self.wavelet_convs[i](curr_x_tag))
curr_x_tag = curr_x_tag.reshape(shape_x)
x_ll_in_levels.append(curr_x_tag[:, :, 0, :, :])
x_h_in_levels.append(curr_x_tag[:, :, 1:4, :, :])
next_x_ll = 0
for i in range(self.wt_levels - 1, -1, -1):
curr_x_ll = x_ll_in_levels.pop()
curr_x_h = x_h_in_levels.pop()
curr_shape = shapes_in_levels.pop()
curr_x_ll = curr_x_ll + next_x_ll
curr_x = torch.cat([curr_x_ll.unsqueeze(2), curr_x_h], dim=2)
next_x_ll = self.iwt_function(curr_x)
next_x_ll = next_x_ll[:, :, :curr_shape[2], :curr_shape[3]]
x_tag = next_x_ll
assert len(x_ll_in_levels) == 0
x = self.base_scale(self.base_conv(x))
x = x + x_tag
if self.do_stride is not None:
x = self.do_stride(x)
return x
class _ScaleModule(nn.Module):
def __init__(self, dims, init_scale=1.0, init_bias=0):
super(_ScaleModule, self).__init__()
self.dims = dims
self.weight = nn.Parameter(torch.ones(*dims) * init_scale)
self.bias = None
def forward(self, x):
return torch.mul(self.weight, x)
if __name__ == '__main__':
block = WTConv2d(in_channels=3, out_channels=3)
input = torch.rand(1, 3, 64, 64)
output = block(input)
print(input.size())
print(output.size())
