Let's say we have a very simple, blurry image represented by a set of numbers (pixel values). We want to remove the blur using a basic trigonometric idea.

Step 1: Understand the blurry image. Imagine a line of pixels with values: [10, 20, 30, 20, 10]. This looks like a simple wave.
---Step 2: Recognize that blur often adds or spreads out pixel values. We can model this blur as a 'smearing' operation.
---Step 3: A trigonometric function, like a sine wave, can also represent repeating patterns. If the blur has a repeating pattern, we can try to find a sine wave that matches it.
---Step 4: Let's assume the blur pattern is similar to a sine wave with a certain 'frequency' (how often it repeats) and 'amplitude' (how strong it is).
---Step 5: Image restoration algorithms use something called Fourier Transform, which breaks down the image into many sine and cosine waves of different frequencies.
---Step 6: They then identify the frequencies associated with the blur and 'filter' them out, effectively subtracting those specific waves from the image.
---Step 7: After removing the blur-related waves, the remaining waves are combined back to form a clearer image. This process relies heavily on the properties of sine and cosine waves.
---Answer: By representing image features and blur as trigonometric waves and manipulating these waves, the blur can be identified and removed.