🖼️ Lossy Image Compression

Interactive JPEG Compression • DCT • Quantization • MSE • PSNR

📚 What is Lossy Compression?

Lossy compression reduces the size of an image by permanently removing some information that is less important to human visual perception.

Key idea: A smaller amount of data is stored, but the reconstructed image may not be exactly identical to the original image.

Original Image → Transformation → Quantization → Encoding → Compressed Image

📤 1. Upload Image

Upload a photograph or other image to demonstrate lossy JPEG compression.

🖼️ 2. Original vs Compressed Image

Original Image

Compressed JPEG

🎚️ 3. JPEG Quality Control

Move the slider to change JPEG compression quality.

80%

Higher quality → larger file → less information loss
Lower quality → smaller file → more information loss

📊 4. Compression Results

- Original Size

- Compressed Size

- Compression Ratio

- Size Reduction

- MSE

- PSNR

Parameter	Result
Image Dimensions	-
JPEG Quality	-
Original File Size	-
Compressed File Size	-
Compression Ratio	-
Size Reduction	-
MSE	-
PSNR	-

⬇️ Download Compressed JPEG

🧮 5. Mathematics of Lossy Compression

Step 1 — DCT

F(u,v) = 1/4 C(u)C(v) Σ Σ f(x,y) cos[(2x+1)uπ/16] cos[(2y+1)vπ/16]

DCT transforms pixel information from the spatial domain into the frequency domain.

Step 2 — Quantization

Q(u,v) = round(F(u,v) / T(u,v))

This is the main lossy operation in JPEG.

Step 3 — Encoding

Quantized Coefficients → Zig-Zag Scan → Run Length Encoding → Huffman Coding

🎯 6. Quantization Example

Suppose a DCT coefficient is:

F(u,v) = 137

T(u,v) = 10

Q(u,v) = round(137 / 10)

Q(u,v) = round(13.7)

Q(u,v) = 14

During reconstruction:

F'(u,v) ≈ 14 × 10

F'(u,v) ≈ 140

Original coefficient = 137
Reconstructed coefficient ≈ 140

Therefore, some information has been lost.

📏 7. Measuring Image Quality

Mean Squared Error — MSE

MSE = (1/N) Σ [I(x,y) − K(x,y)]²

Lower MSE means the compressed image is closer to the original image.

Peak Signal-to-Noise Ratio — PSNR

PSNR = 10 log₁₀(MAX² / MSE)

For an 8-bit image:

MAX = 255

Higher PSNR generally means better reconstructed image quality.

🔄 8. JPEG Lossy Compression Pipeline

RGB Image

→

YCbCr

→

8×8 Blocks

→

DCT

→

Quantization

→

Zig-Zag

→

RLE

→

Huffman

→

JPEG

⚖️ 9. Lossless vs Lossy Compression

Feature	Lossless	Lossy
Information Loss	No	Yes
Original Recovery	Exact	Not exact
File Size	Moderate	Usually smaller
Quality	Original quality	Depends on compression
Examples	PNG, RLE, Huffman	JPEG

✅ 10. Advantages of Lossy Compression

• Significantly reduces image file size.
• Reduces storage requirements.
• Reduces network transmission time.
• Useful for websites and online applications.
• JPEG provides adjustable quality levels.

⚠️ Disadvantages

• Some information is permanently removed.
• Repeated compression can reduce quality.
• Very high compression can produce visible artifacts.
• The original image cannot be reconstructed exactly.

Created by Bijan Krishna Paul
B.K.PAUL Bhairab Ganguly College