Image compression is rooted in information theory, a field pioneered by Claude Shannon in 1948. Shannon entropy defines the theoretical minimum number of bits needed to represent data without loss, calculated as the negative sum of each symbol probability multiplied by the logarithm base 2 of that probability. For image data, this means the more predictable or repetitive the pixel values, the fewer bits are needed to represent them. A solid white image has very low entropy and compresses to almost nothing, while a photograph of a complex natural scene has high entropy and requires more bits.

Lossless compression algorithms like those used in PNG exploit statistical redundancy using techniques such as Huffman coding and arithmetic coding. Huffman coding assigns shorter bit sequences to more frequently occurring pixel values and longer sequences to rare values, reducing the average bits per pixel. For example, if a particular shade of blue appears in 40% of pixels, Huffman coding might represent it with just 2 bits instead of the standard 8 bits per channel, yielding significant savings. Run-length encoding (RLE) is another technique that replaces sequences of identical values with a count-value pair.

Lossy compression goes further by exploiting the psychovisual model of human perception. The human visual system has well-documented limitations: we are more sensitive to brightness changes than color changes, more sensitive to low-frequency patterns than high-frequency detail, and less able to perceive differences in very dark or very bright regions. JPEG quantization tables are specifically designed around these perceptual characteristics, discarding high-frequency information that falls below the threshold of human perception.

Measuring compression quality objectively requires perceptual quality metrics. Peak Signal-to-Noise Ratio (PSNR) measures the ratio between maximum possible pixel value and the error introduced by compression, expressed in decibels. Values above 40 dB generally indicate imperceptible quality loss. However, PSNR treats all pixel errors equally regardless of perceptual significance. The Structural Similarity Index (SSIM) is a more sophisticated metric that compares luminance, contrast, and structural information between original and compressed images, producing a score from 0 to 1 where values above 0.95 typically indicate excellent perceptual quality. SSIM better correlates with human perception because it considers how the human visual system processes structural patterns rather than individual pixel differences.