Understanding gain of the DCT transform

1. How does the Discrete Cosine Transform work?
2. What is DCT how DCT helps to achieve compression?
3. What is the DCT coefficient?
4. Why is DCT Discrete Cosine Transform a more popular transform for compression though KLT Karhunen Loeve transform is optimal?

How does the Discrete Cosine Transform work?

The DCT works by separating images into parts of differing frequencies. During a step called quantization, where part of compression actually occurs, the less important frequencies are discarded, hence the use of the term “lossy.

What is DCT how DCT helps to achieve compression?

DCT is used in the JPEG image compression algorithm. The input image is divided into 8-by-8 or 16-by-16 blocks, and the two-dimensional DCT is computed for each block. The DCT coefficients are then quantized, coded, and transmitted.

What is the DCT coefficient?

DCT coefficient (0,0) is the DC coefficient, or average sample value. Since natural images tend to vary only slightly from sample to sample, low frequency coefficients are typically larger values and high frequency coefficients are typically smaller values. The 8×8 DCT is defined in Figure 5.21.

Why is DCT Discrete Cosine Transform a more popular transform for compression though KLT Karhunen Loeve transform is optimal?

DCT is the closest approximation to the KL Transform. Mostly we are interested in low frequency signals so only even component is necessary hence its computationally feasible to compute only DCT.