An outline of JPEG compression

"There are many options for JPEG compression and many parameters that may be specified. [The] goal [here] is not a “bit-by-bit” account of the algorithm but rather to illustrate the role of the mathematics [involved], specifically the DCT. Here is the basic procedure:

1. Separate color, if applicable: A color image is decomposed into its color components, usually using the YCbCr color scheme. This color representation scheme, like RGB, dictates the color of each pixel with three numbers. The entire image can thus be represented by three arrays of appropriate size. The details here need not concern us, since we will be working with monochrome images.
2. Transform: Perform a block DCT on the image using 8 × 8 pixel blocks. If the image pixel count in either dimension is not a multiple of 8 the image is padded in some way to a higher multiple of 8. 
3. Quantize: Each 8 × 8 pixel block has an 8 × 8 DCT consisting of real numbers. Each of the 64 components or frequencies in this DCT is quantized. This is the main lossy step in the compression.
4. Compress: The image is compressed by using run-length encoding on each block, and then Huffman coding the result. The dc coefficient is often treated separately. This is the step where actual file compression occurs.

Decoding reverses the steps:
4. Decompress: Recover the quantized DCT blocks.
3. Dequantize.
2. Inverse transform: Apply the inverse DCT to each block.
1. Mix colors: If applicable, and display block."

From Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing by S. Allen Broughton and Kurt M. Bryan.