Poisson Noise

Easy:

Imagine you are taking pictures with your toy camera, and sometimes the number of stars in the night sky looks different even if you take two photos at the same time. This is because of something called “noise,” which can make images look less clear or more grainy than they would otherwise.

Poisson noise(pronounced Pwuh-SWAH noise) is one type of noise that can happen when we take pictures or create digital images using sensors that detect light. It happens because light itself is made up of tiny particles called photons, and each sensor can only count a certain number of these photons before it gets full. So, if there aren’t enough photons hitting the sensor, the image can end up looking noisy or grainy.

In deep learning, Poisson noise can be an issue because it can affect how well our models can recognize objects in images. That’s why researchers often try to remove or reduce this kind of noise as part of their work. By doing so, they can help ensure that the models they build will be more accurate and reliable.

Moderate:

Poisson noise is a type of statistical noise that occurs when events occur in a given time interval with a constant mean rate, and follows a Poisson distribution. This concept is named after Simeon Poisson, who developed the theory behind it. In simpler terms, imagine you’re throwing darts at a dartboard. If you throw one dart per minute and you keep doing this for a long time, the number of times you hit the bullseye will follow a Poisson distribution. This is because the likelihood of hitting the bullseye in any given minute is constant; it doesn’t change based on whether you’ve already hit it or not.

In the context of deep learning and image processing, Poisson noise often appears in images captured by cameras, especially in low-light conditions. When light hits a camera sensor, it generates electrons. If the exposure time is too short, not enough electrons are generated, leading to underexposed images. Conversely, if the exposure time is too long, the sensor can accumulate too many electrons, resulting in overexposure and loss of detail. Both scenarios introduce noise into the image data, which can affect the quality of the processed output.

To handle Poisson noise in deep learning applications, such as enhancing images or videos, models need to be trained specifically to recognize and mitigate its effects. This involves adjusting the model architecture and training process to account for the statistical properties of Poisson noise, ensuring that the final output is clearer and more accurate despite the presence of noise.

Hard:

Poisson Noise, also known as “shot noise,” is a type of noise that occurs when the number of events (like the arrival of photons in a camera sensor) is very small. It is named after the French mathematician Siméon Denis Poisson, who described the statistical distribution of rare events.

What is Poisson Noise?

1. Randomness of Events: Imagine you’re counting raindrops falling into a small bucket over short periods. Sometimes, you’ll get 2 drops, sometimes 5, and sometimes none at all. This variation is random and can be described by Poisson distribution. The same idea applies to photons (light particles) hitting a camera sensor or other detectors.

2. Poisson Distribution: In mathematical terms, Poisson distribution describes the probability of a given number of events happening in a fixed interval of time or space. If the average number of events (like raindrops or photons) is λ (lambda), the probability of observing k events is given by the formula mentioned at the end of this article. This formula helps us understand how likely it is to get a certain number of events when the average rate (λ) is known.

3. Characteristics of Poisson Noise:
   Discrete Events: It deals with counts of events that happen independently.
   Variance Equals Mean: In Poisson distribution, the variance (a measure of how spread out the counts are) is equal to the mean (average count).

Poisson Noise in Deep Learning

In the context of deep learning, Poisson Noise can affect the quality of the data (like images) that models learn from:

1. Image Sensors: When capturing images, especially in low-light conditions, the number of photons hitting each pixel can vary according to Poisson statistics. This results in grainy or noisy images.

2. Training Models: When training neural networks, it’s important for the models to learn to distinguish between real patterns in the data and the random noise. If a model overfits to the noise, it won’t perform well on new, unseen data.

3. Data Augmentation: Sometimes, Poisson Noise is intentionally added to training data as a form of augmentation. This helps make the model more robust and better at handling real-world scenarios where noise is present.

Simplified Example

Imagine you have a small box and you’re counting how many marbles drop into it every second. If you count 3 marbles in one second and 5 marbles in the next, there’s a bit of randomness in your counts. Poisson Noise is like this randomness in counting the marbles.

In summary, Poisson Noise is a type of randomness that comes from counting rare events, and it’s important for deep learning models to learn to handle this noise to make accurate predictions.

A few books on deep learning that I am reading:

Book 1

Book 2

Book 3