论文阅读 | CSNet

CSNet

HIT TIP 2020

Architecture

Overview

Highlights:

• end-to-end mapping
• encoder-decoder
• block-based compressed sensing (BCS)
• non-overlapping. (有什么好处，为什么一直强调)

3 stages:

• Conpressied Sampling
• Initial Reconstruction
• Non-linear Signal Reconstruction

Sampling Network

Refered as \(\mathcal{S}\).

Training Phase

学习采样矩阵并获取 CS 测量值。端到端地构建采样网络与重建网络，联合训练并优化 (joint optimization)，区别于 ISTA-Net 针对已知 Sampling Matrix 进行重建。

Application Phase

Used as an encoder to generate CS measurements.

对 \(B\times B\times l\) 的块，这里用 \(\text{stride}= B\) 的卷积代替了采样矩阵。不需要学习数据的偏移，即

bias=False

采样矩阵 \(\Phi_B \in \mathbb{R}^{n_B\times lB^2}\)，特征图共 \(n_B=\lfloor \frac{M}{N}lB^2\rfloor\) 个。\(l\) 取 1 即为灰度图。

Reconstruction Network

Refered as \(\mathcal{R}\).

\[\mathcal{R}(\mathbf{y})=\mathcal{D}(\mathcal{I}(\mathbf{y})) \tag{1} \]

where \(\mathbf{y}\) the output of \(\mathcal{S}\), \(\mathcal{D}\) the deep construction network, \(\mathcal{I}\) the initial reconstruction network.

Initial Reconstruction Network

“Given the CS measurements, BCS usually uses a pseudo-inverse matrix to obtain the initial reconstructed image.”

指出，本质上实在求 CS 采样矩阵的伪逆。(但是由 \(M \ll N\)，问题欠定，如何确保风格一致呢)

CS 正问题如下

\[\mathbf{y}=\Phi_B\textbf{x} \tag{2} \]

因此对第 \(j\) 块的 CS 测量值 \(\mathbf{y}_j^{lB^2}\)

\[\tilde{\mathbf{x}_j}=\tilde{\Phi}_B\mathbf{y}_j \tag{3} \]

\(\tilde{\Phi}_B\) refered as \(\tilde{\mathcal{I}}\)，如下

torch.nn.Conv2d(
    in_channels=n_B,
    out_channels=lB^2,
    kernel_size=1,
    stride=1,
    padding=0,
    biad=False
)

然后进行 reshape 和 concat 得到 \(\tilde{\mathbf{x}}=\mathcal{I}(\mathbf{y})\)

这里还提到，“makes our method can make full use of both intra-block and interblock information for better reconstruction.” (别的网络做不到吗)

Deep Reconstruction Network

相较于 ISTA-Net 和 AMP-Net，多了残差连接。

Training

介绍了二进制采样矩阵 (0, 1) 和极性采样矩阵 (+, -) 的训练方式。

Loss Function

分别对 \(\mathcal{I}(\cdot)\) 和 \(\mathcal{R}(\cdot)\) 应用 \(\ell_2\) 损失。