# 4.4. 正则化成像方法¶

## 4.4.1. 正则化成像¶

SAR imaging process can be formulated as

${\bm s} = {\bm A}{\bm g},$

where, $${\bm s}$$ is the $$MN\times 1$$ recieved SAR raw data vector in phase history domain, $$\bm g$$ is the $$HW \times 1$$ reflection vector of scene, and $$\bm A$$ represents the the mapping from scene to SAR raw data.

Given $$\bm s, \bm A$$ , regularization methods try to reconstruct $$\bm g$$ by minmizing

$\mathop {\rm min}\limits_{\bm{g}} {\left\| {{\bm{Ag}} - {\bm{s}}} \right\|_2} + \lambda |{\bm{g}}{|_p},$

where, $$\lambda$$ is the balance factor, and $$|\cdot|_p$$ is the $$\ell_p$$ norm.

Note that, if $${\bm s, A, g} \in {\mathbb C}$$ , the problem changes to

${\mathop{\rm Re}\nolimits} ({\bm{s}}) + j{\rm Im}({\bm{s}}) = {\rm Re}({\bm{Ag}}) + j{\mathop{\rm Im}\nolimits} ({\bm{Ag}})$

so we have:

$\left[ {\begin{array}{ccc} {{\mathop{\rm Re}\nolimits} ({\bm{s}})}\\ {{\mathop{\rm Im}\nolimits} ({\bm{s}})} \end{array}} \right] = \left[ {\begin{array}{ccc} {{\mathop{\rm Re}\nolimits} ({\bm{A}})}&{ - {\mathop{\rm Im}\nolimits} ({\bm{A}})}\\ {{\rm Im}({\bm{A}})}&{{\mathop{\rm Re}\nolimits} ({\bm{A}})} \end{array}} \right]\left[ {\begin{array}{ccc} {{\mathop{\rm Re}\nolimits} ({\bm{g}})}\\ {{\mathop{\rm Im}\nolimits} ({\bm{g}})} \end{array}} \right]$

## 4.4.2. 实验与分析¶

### 实验说明¶

• 仿真场景大小: $$32 \times 32$$

• 回波矩阵大小: $$32 \times 32$$

• 稀疏表示字典: 无, DCT , DWT

• 优化方法: Lasso , OMP

### 实验代码¶

iprs2.0 demo_regular_sar.py

• 运行时间:

• 重构误差: