feat: add Peak Signal-to-Noise Ratio (PSNR) to compression (#1028)

Author: AliAlimohammadi

DIRECTORY.md

@@ -69,6 +69,7 @@
     * [Huffman Encoding](https://github.com/TheAlgorithms/Rust/blob/master/src/compression/huffman_encoding.rs)
     * [LZ77](https://github.com/TheAlgorithms/Rust/blob/master/src/compression/lz77.rs)
     * [Move to Front](https://github.com/TheAlgorithms/Rust/blob/master/src/compression/move_to_front.rs)
+    * [Peak Signal-to-Noise Ratio](https://github.com/TheAlgorithms/Rust/blob/master/src/compression/peak_signal_to_noise_ratio.rs)
     * [Run Length Encoding](https://github.com/TheAlgorithms/Rust/blob/master/src/compression/run_length_encoding.rs)
   * Conversions
     * [Binary to Decimal](https://github.com/TheAlgorithms/Rust/blob/master/src/conversions/binary_to_decimal.rs)

src/compression/mod.rs

@@ -2,10 +2,12 @@ mod burrows_wheeler_transform;
 mod huffman_encoding;
 mod lz77;
 mod move_to_front;
+mod peak_signal_to_noise_ratio;
 mod run_length_encoding;
 
 pub use self::burrows_wheeler_transform::{all_rotations, bwt_transform, reverse_bwt, BwtResult};
 pub use self::huffman_encoding::{huffman_decode, huffman_encode};
 pub use self::lz77::{LZ77Compressor, Token};
 pub use self::move_to_front::{move_to_front_decode, move_to_front_encode};
+pub use self::peak_signal_to_noise_ratio::peak_signal_to_noise_ratio;
 pub use self::run_length_encoding::{run_length_decode, run_length_encode};

src/compression/peak_signal_to_noise_ratio.rs

@@ -0,0 +1,93 @@
+//! # Peak Signal-to-Noise Ratio (PSNR)
+//!
+//! Measures the quality of a reconstructed or compressed image relative to the original.
+//! A higher PSNR generally indicates better quality.
+//!
+//! Reference: <https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio>
+
+const PIXEL_MAX: f64 = 255.0;
+
+/// Computes the PSNR in decibels (dB) between an original and a compressed image.
+///
+/// # Arguments
+/// * `original` - Pixel values of the original image (u8 slice, any channel layout)
+/// * `compressed` - Pixel values of the compressed/reconstructed image (same length)
+///
+/// # Returns
+/// * `f64::INFINITY` when the images are identical (MSE = 0)
+/// * Otherwise the PSNR value in dB
+///
+/// # Panics
+/// Panics if `original` and `compressed` have different lengths.
+pub fn peak_signal_to_noise_ratio(original: &[u8], compressed: &[u8]) -> f64 {
+    assert_eq!(
+        original.len(),
+        compressed.len(),
+        "original and compressed images must have the same number of pixels"
+    );
+
+    let mse: f64 = original
+        .iter()
+        .zip(compressed.iter())
+        .map(|(&o, &c)| {
+            let diff = o as f64 - c as f64;
+            diff * diff
+        })
+        .sum::<f64>()
+        / original.len() as f64;
+
+    if mse == 0.0 {
+        return f64::INFINITY;
+    }
+
+    20.0 * (PIXEL_MAX / mse.sqrt()).log10()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn identical_images_returns_infinity() {
+        let img = vec![100u8, 150, 200, 50, 75, 25];
+        assert_eq!(peak_signal_to_noise_ratio(&img, &img), f64::INFINITY);
+    }
+
+    #[test]
+    fn single_pixel_off_by_one() {
+        // original: [0], compressed: [1]  →  MSE = 1.0  →  PSNR = 20·log10(255) ≈ 48.13 dB
+        let original = vec![0u8];
+        let compressed = vec![1u8];
+        let psnr = peak_signal_to_noise_ratio(&original, &compressed);
+        let expected = 20.0 * 255.0_f64.log10();
+        assert!((psnr - expected).abs() < 1e-6, "got {psnr}");
+    }
+
+    #[test]
+    fn uniform_noise() {
+        // original all-zero, compressed all-10  →  MSE = 100  →  PSNR = 20·log10(255/10) ≈ 28.13 dB
+        let original = vec![0u8; 16];
+        let compressed = vec![10u8; 16];
+        let psnr = peak_signal_to_noise_ratio(&original, &compressed);
+        let expected = 20.0 * (PIXEL_MAX / 10.0).log10();
+        assert!((psnr - expected).abs() < 1e-6, "got {psnr}");
+    }
+
+    #[test]
+    fn known_psnr_value() {
+        // 4 pixels: diffs = [15, 15, 15, 15]  →  MSE = 225  →  PSNR ≈ 24.61 dB
+        let original = vec![0u8, 0, 0, 0];
+        let compressed = vec![15u8, 15, 15, 15];
+        let psnr = peak_signal_to_noise_ratio(&original, &compressed);
+        let expected = 20.0 * (PIXEL_MAX / 15.0).log10();
+        assert!((psnr - expected).abs() < 1e-6, "got {psnr}");
+    }
+
+    #[test]
+    #[should_panic(expected = "same number of pixels")]
+    fn mismatched_lengths_panics() {
+        let original = vec![0u8; 4];
+        let compressed = vec![0u8; 8];
+        peak_signal_to_noise_ratio(&original, &compressed);
+    }
+}