Let's look at the way PCA works, when the algorithm does not act as a data processing stage, but as the main stage. The task of noise reduction in images is just that case.
The pipeline in this case looks like this: you load the noisy data into the model, after which you can process other data using PCA and the model will restore that data. How it works? By reducing the number of main components - literally only the most “important” elements of the image remain, i.e. noise will be reduced.
We use the USPS dataset with numbers and the `scikit-learn` library:

```python
import numpy as np
from sklearn.datasets import fetch_openml
from sklearn.preprocessing import MinMaxScaler
from sklearn.model_selection import train_test_split

X, y = fetch_openml(data_id = 41082, as_frame = False, return_X_y = True)
X = MinMaxScaler().fit_transform(X)
```

```python
X_train, X_test, y_train, y_test = train_test_split(
    X, y, stratify = y, random_state = 0, train_size = 1_000, test_size = 100
)

rng = np.random.RandomState(0)
noise = rng.normal(scale = 0.25, size = X_test.shape)
X_test_noisy = X_test + noise

noise = rng.normal(scale = 0.25, size = X_train.shape)
X_train_noisy = X_train + noise 
```

from sklearn.decomposition import PCA

pca_model = PCA(n_components=40)
pca_model.fit(X_train_noisy)

Let's see what came of it! Initial noisy images:

Is the PCA method designed to reduce noise in the data?

Let's take a look at PCA (Principal Component Analysis) from afar. In this section, you will learn what PCA is, why this data processing method is needed and see the real problems it solves.

Learn about the design of the PCA algorithm. This section will show each stage in detail and simply.

Set up your first PCA model using the Python library and solve the challenge provided for you.

It's time to find out how we can explain the results. What do the first, second and third components tell us? What can we use the data for in the future?