﻿ 关于合成孔径雷达图像的量化位数和量化方法选择

# 关于合成孔径雷达图像的量化位数和量化方法选择Choosing the Quantization Bit and Quantization Method of Synthetic Aperture Radar Image

Abstract: After the echoes of micro SAR (Synthetic Aperture Radar) equipment are focused, in order to facilitate storage and secondary processing, an effective down-sampling method is studied to increase the image processing rate while reducing the loss of image quality. This article briefly introduces the selection of micro-miniaturized synthetic aperture radar image storage bits, analyzes the relationship between image storage bits and image quality from two aspects of read rate and algorithm processing efficiency, and elaborates the synthetic aperture radar image down sampling method in detail, and simulates the signal-to-noise ratio and quantization noise corresponding to different quantization methods. According to the simulation results, the non-uniform quantization method proposed in the article is a down sampling method that can improve the volume-to-noise ratio.

1. 引言

2. 轻小型化SAR存储位数的选择

2.1. SAR系统结构对存储位数选择有影响

Figure 1. Schematic diagram of continuous wave radar structure

Figure 2. Diagram of the various parts of the synthetic aperture radar system

2.2. 量化位数的改变对信噪比带来的影响

2.2.1. 量化信噪比

${V}_{\text{A/D}}=\frac{{V}_{\text{LSB}}}{\sqrt{12}}$

${N}_{q}=E\left[{\left({m}_{k}-{m}_{q}\right)}^{2}\right]=\underset{a}{\overset{b}{\int }}{\left({m}_{k}-{m}_{q}\right)}^{2}f\left({m}_{k}\right)\text{d}{m}_{k}=\underset{i=1}{\overset{M}{\sum }}\underset{{m}_{i-1}}{\overset{{m}_{i}}{\int }}{\left({m}_{k}-{q}_{i}\right)}^{2}f\left({m}_{k}\right)\text{d}{m}_{k}$

$SNR=\frac{{S}_{0}}{{N}_{q}}=\frac{E\left({m}_{k}^{2}\right)}{E\left[{\left({m}_{k}-{m}_{q}\right)}^{2}\right]}=\frac{\underset{a}{\overset{b}{\int }}{m}_{k}^{2}f\left({m}_{k}\right)\text{d}{m}_{k}}{\underset{a}{\overset{b}{\int }}{\left({m}_{k}-{m}_{q}\right)}^{2}f\left({m}_{k}\right)\text{d}{m}_{k}}=\frac{\underset{a}{\overset{b}{\int }}{m}_{k}^{2}f\left({m}_{k}\right)\text{d}{m}_{k}}{\underset{i=1}{\overset{M}{\sum }}\underset{{m}_{i-1}}{\overset{{m}_{i}}{\int }}{\left({m}_{k}-{q}_{i}\right)}^{2}f\left({m}_{k}\right)\text{d}{m}_{k}}$

2.2.2. 目标检测算法速度

Table 1. Detection speed result data

3. 存储位数变换方法

3.1. 基于均匀量化位数变换方法

$\begin{array}{l}{R}_{1}=\left(-\infty ,a\right]\\ {R}_{2}=\left(a,a+\Delta \right]\\ {R}_{3}=\left(a+\Delta ,a+2\Delta \right]\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}⋮\\ {R}_{N}=\left(a+\left(N-2\right)\Delta ,+\infty \right]\end{array}$

$\Delta v=\frac{b-a}{M}$

${m}_{i}=a+i\Delta v,\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=0,1,\cdots ,M$

${q}_{i}=\frac{{m}_{i}+{m}_{i-1}}{2},\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1,2,\cdots ,M$

64位转换为8位，基于通用计算机软件方法。

16位转换为8位，专用SAR成像处理系统。

${v}_{qn}=\sqrt{\frac{1}{Q}\underset{-\frac{Q}{2}}{\overset{+\frac{Q}{2}}{\int }}{x}^{2}\text{d}x}=\sqrt{\frac{1}{Q}{\left[\frac{{x}^{3}}{3}\right]|}_{-\frac{Q}{2}}^{+\frac{Q}{2}}}=\sqrt{\frac{{Q}^{2}}{{2}^{3}×3}+\frac{{Q}^{2}}{{2}^{3}×3}}=\frac{Q}{\sqrt{12}}$

3.2. 基于非均匀压缩的位数变换方法

A律对数量化器：

$f\left(x\right)=\left\{\begin{array}{l}\frac{Ax}{1+\mathrm{ln}A},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }\text{\hspace{0.17em}}0\le x\le 1/A\\ \frac{1+\mathrm{ln}Ax}{1+\mathrm{ln}A},\text{\hspace{0.17em}}\text{\hspace{0.17em}}1/A\le x\le 1\end{array}$

4. 基于MATLAB的仿真实验

Figure 3. Schematic diagram of non-uniform compressed bit transformation

Figure 5. All image data distribution

Figure 6. 8 bit uniform quantization result

Figure 7. 8-bit non-uniform quantization result

Figure 8. Compression of all image data

Table 2. Comparison of different quantitative results

5. 结束语

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