Suppose that a digital image has 5 x 5 pixels with 8-bit grayscale level. The pixel values of the image are given below. 255 160 160 255 255 51 51 160 160 160 51 51 160 160 0 160 160 51 255 160 255 255 255 *Do this question manually. You may use a calculator but do not use Matlab functions. (a) How many total bytes does this image have? (b) Sketch the histogram. (C) Sketch the standard histogram (probability density function). (d) Calculate the entropy of the image Now, we want to compress the image as much as possible using a variable-length encoding scheme (Huffman coding) with the 4 code values. The new code values are given as: 0, 10, 110, and 111. (e) Assign the given new code to each pixel value to minimize the image file size. (f) Calculate the average code length with the new codes. (g) When these codes are used, calculate the compression ratio. (h) Is this lossless or lossy compression? Justify your answer. Suppose that a digital image has 5 x 5 pixels with 8-bit grayscale level. The pixel values of the image are given below. 255 160 160 255 255 51 51 160 160 160 51 51 160 160 0 160 160 51 255 160 255 255 255 *Do this question manually. You may use a calculator but do not use Matlab functions. (a) How many total bytes does this image have? (b) Sketch the histogram. (C) Sketch the standard histogram (probability density function). (d) Calculate the entropy of the image Now, we want to compress the image as much as possible using a variable-length encoding scheme (Huffman coding) with the 4 code values. The new code values are given as: 0, 10, 110, and 111. (e) Assign the given new code to each pixel value to minimize the image file size. (f) Calculate the average code length with the new codes. (g) When these codes are used, calculate the compression ratio. (h) Is this lossless or lossy compression? Justify your