DCT as a Separable Image Transform for Compression

The image is first divided into 8x8 pixel blocks, with each block undergoing Discrete Cosine Transform (DCT). DCT is a separable transform method widely used in image compression coding, operating by converting spatial domain image data into frequency domain coefficients. This transformation concentrates energy in low-frequency components, enabling efficient compression through quantization of higher-frequency coefficients. Following DCT transformation, the image undergoes Inverse Discrete Cosine Transform (IDCT) for decompression operations. IDCT reconstructs the original image by converting frequency domain coefficients back to spatial domain data. In practical implementation, this typically involves: - Applying 2D DCT to each block using matrix operations: block_dct = T * block_data * T' where T is the DCT transformation matrix - Quantizing DCT coefficients using a quantization table to reduce data size - Applying IDCT using the inverse transformation: reconstructed_block = T' * quantized_coefficients * T This block-based approach allows efficient image compression and decompression while maintaining visual quality through controlled quantization parameters. The separation property of DCT enables efficient computation by applying 1D transforms sequentially to rows and columns.