and sigmoid activation to obtain the spatial attention map $\mathbf{\hat{f}} \in \mathbb{R}^{H\times W \times 1}$, which we then use to rescale $\mathbf{M}$.

**Residual resizing modules.** The proposed framework employs a recursive residual design (with skip connections) to ease the flow of information during the learning process. In order to maintain the residual nature of our architecture, we introduce residual resizing modules to perform downsampling (Fig. \[fig:downsample\]) and upsampling (Fig. \[fig:upsample\]) operations. In MRB, the size of feature maps remains constant along convolution streams. On the other hand, across streams the feature map size changes depending on the input resolution index $i$ and the output resolution index $j$. If $i<j$, the input feature tensor is downsampled, and if $i>j$, the feature map is upsampled. To perform $2\times$ downsampling (halving the spatial dimension and doubling the channel dimension), we apply the module in Fig. \[fig:downsample\] only once. For $4\times$ downsampling, the module is applied twice, consecutively. Similarly, one can perform $2\times$ and $4\times$ upsampling by applying the module in Fig. \[fig:upsample\] once and twice, respectively. Note in Fig. \[fig:downsample\], we integrate anti-aliasing downsampling [@zhang2019making] to improve the shift-equivariance of our network.

[0.49]{} ![image](Images/downsample.png){width="\textwidth"}

[0.49]{} ![image](Images/upsample.png){width="\textwidth"}

Experiments
===========

In this section, we perform 