Image Restoration

Image Restoration

English translation by SOTA – AI Community of the Russian original. Licensed MIT, like the original. Organisers who would like this translation removed can email [email protected].

Contest 1 (25 June 2025) of the Kazakhstan IOAI Team Selection Test (Отборочные на IOAI), 2025. This is the Overview tab of the Kaggle competition "Upsolving TST Day 1" (subtitle: "Up Solving for TST Day 1"), the host's public upsolving copy of the contest, open from 25 June to 1 September 2025. Original: kaggle.com/competitions/up-solving-tst-day-1. The Data tab is translated in a separate file.

Overview

Statement

You have an image of size 128×128 in RGB format (three channels). However, one of 12 colour filters of size 2×2 has been applied to it.

Each filter determines which channel (R, G or B) is kept in each of the 4 cells of a 2×2 block, and the other channels are zeroed. All the other pixels at these positions in the other channels are set to zero (become 0).

Task

You are given an image after the filter has been applied. It is known that the same filter was used over the whole image, but which one is unknown.

Your task is to:

• Determine which of the 12 possible filters was applied.
• Reconstruct an approximation of the original image.

💻 The starter notebook is available here: https://www.kaggle.com/code/akhanov/tst-day1-starter

Description

Filter properties:

• A filter is a list of four symbols: ['R', 'G', 'B', 'R'].

• These symbols determine which channel is kept in the:

  • top-left (0, 0),
  • top-right (0, 1),
  • bottom-left (1, 0),
  • bottom-right (1, 1) pixels of a 2×2 block.

• It is guaranteed that:

  • The filter contains all three channels (R, G, B) at least once.
  • Identical letters lie on a diagonal (either the main diagonal or the anti-diagonal).
  • There are 12 possible filters in total that satisfy these conditions.

Filter example:

['R', 'G',
 'B', 'R']

This means:

• Pixel (0,0) keeps only the red (R) channel.
• Pixel (0,1) keeps green (G).
• Pixel (1,0) keeps blue (B).
• Pixel (1,1) keeps red (R).

Applying the filter

The filter is applied to the whole image in 2×2 blocks, that is:

• (0,0)-(1,1), (0,2)-(1,3), ..., (126,126)-(127,127)
• The filter is applied with the same rules on every 2×2 block.

Example filtering code:

def apply_fast_filter(img, pattern):
    """Applies a 2x2 filter to an image."""
    # Create a new image with the same dimensions
    filtered_img = np.zeros_like(img)
    
    # For each pixel in the 2x2 block, keep only the required channel
    # Top left
    filtered_img[0::2, 0::2, pattern[0]] = img[0::2, 0::2, pattern[0]]
    # Top right
    filtered_img[0::2, 1::2, pattern[1]] = img[0::2, 1::2, pattern[1]]
    # Bottom left
    filtered_img[1::2, 0::2, pattern[2]] = img[1::2, 0::2, pattern[2]]
    # Bottom right
    filtered_img[1::2, 1::2, pattern[3]] = img[1::2, 1::2, pattern[3]]
    
    return filtered_img

Here pattern is a list of channel indices (0 — R, 1 — G, 2 — B), for example [0, 1, 1, 0] instead of ['R', 'G', 'G', 'R'].

Evaluation

📏 Metric

The metric in this task is PSNR (Peak Signal-to-Noise Ratio) between the reconstructed image and the original.

$$\text{PSNR}(I, \hat{I}) = 10 \cdot \log_{10} \left( \frac{255^2}{\text{MSE}(I, \hat{I})} \right)$$

where:

• I is the original image (before the filter was applied),
• Î is the image reconstructed by the participant,
• H, W, C are the height, width and number of channels (in this task: 128×128×3),
• All pixel values are from 0 to 255 (type uint8).

$$\text{MSE}(I, \hat{I}) = \frac{1}{H \cdot W \cdot C} \sum_{x=1}^{H} \sum_{y=1}^{W} \sum_{c=1}^{C} \left( I_{x,y,c} - \hat{I}_{x,y,c} \right)^2$$

• All image values lie in the range from 0 to 255 (type uint8).

The higher the PSNR value, the better the reconstruction quality.