1. Noise Type

Gaussian Noise

And unfortunately it's not, actually there's not real physical systems that produce Gaussian noise. So, why is this such an important noise?

mathematically, very easy to work with
good approximation to other types of noise, especially for small regions of image or small region of pixel values

Rayleigh Noise

z^-是Rayleigh噪声的均值
σ是方差
Rayleigh Noise normally is used to model noise in certain areas of magnetic resonant imaging. This is a good model for real physical devices.

Exponential Noise

Uniform Noise

选区_048.jpg

Uniform是量化噪声的模型, Exponential是预测编码的噪声模型
Noise有时是从设备中产生的, 比如传感器噪声, 有时是源于我们对于图像的操作, 比如量化

Pepper Noise

with certain probability you change the pixel completely to a new value. And with certain other probability, you change it to a different value. For example, we start that I go over the image and with certain probability I'd change the pixel, let's say to white, and with other probability I change the pixel, let's say to black and that's why it's called salt and pepper. If I changed it to white that's called salt, and if I changed it to black, that's called pepper. 就是在椒和盐之间来回跳跃, 所以叫椒盐噪声, 椒盐噪声对有些像素影响很大, 而有些完全没有影响, 当它产生影响时, 影响的程度是相同的, 它model的场景是传感器以一个很低的概率出故障, 或者某个像素烧坏了

2. Noise & Histograms

图片.png

原图的histogram是三个δ函数, 就是只有三个peak, 加入噪声后会在这三个peak附近形成与噪声概率分布函数相似的形状(a shape very similar to the actual probability distribution function around each one of the pixel values)

图片.png

为什么要讲噪声和直方图的关系, 是因为通过直方图我们可以来估计噪声的种类和噪声的参数

3. Estimating noise

图片.png

如果我们知道噪声的类型, 那我们直接就通过直方图去算噪声参数, 然后根据噪声类型和参数来选取滤波器, 比如Gaussian Noise可能NLM的效果会比较好, 中值滤波器对Pepper Noise效果比较好, , if we don`t know the type of noise, 我们的做法就是try, we basically go and fit using standard tools for function fitting, we basically fit the best of each one of the distribution. 那这个时候NR就是一个信号拟合问题, 用这些标准的噪声分布函数来拟合信号, 哪一个产生的误差最小, 我们就选择哪一个, 有可能不完全是原来的噪声分布, 但是我们希望这是一个对噪声的较好近似