In a simple image compression scheme, vector quantization (VQ) is used to compress a class of 2-bit grayscale images, with gray levels of 0,1,2 and 3 . A given image is partitioned into 22 blocks (subimages), and encoded using 22 code vectors from a generated codebook. The codebook used in this VQ scheme, together with the associated probabilities of occurrences for the code vectors are given as follows: (a) Huffman coding is used to encode the symbols or indices of the codevectors. Recommend a suitable set of Huffman codewords to encode the symbols based on the probability distribution given in the table above. Your answer should clearly outline all the steps and calculations involved. (14 marks) (b) Test the designed Huffman codeword recommended in part (a). (i) Compute the average number of bits that is required to represent a symbol. (6 marks) (ii) Calculate the average compression ratio of this VQ scheme