Question

Typical ultrasound consists of about 25 images extracted from a full-motion ultrasound examination. Each of these images consists of 512 by 512 pixels, each with 8 bit intensity information. a) What is the total number of bits in the 25 images?

b) Ideally the doctors would like to playback the ultrasounds at 30 frames per second. Assuming that when playing back each ultrasound frame is compressed by a factor of 0.8, what is the data rate required to play the ultrasound?

c) Consider now that this ultrasound needs to be viewed in real-time at a remote location using wireless communication. If the communication system has a signals to noise ration of 30dB and an overhead of 15%, what is the minimum bandwidth required for this communication.

d) Assume a practical error correction method is able to achieve a 75% of the above data rate. How many signal levels are required to achieve this data rate?

Answer 1

a) Total no. of bits in 25 images

= 25 x 512 x 512 x 8

= 52428800

b) 30 frames pers second with each frame containing no. of bits obtained in a) and each frame compressedby a factor 0.8

data rate required to play the sound = 52428800 x 30x 0.8 bits/second

                                                            = (52428800 x 30 x 0.8)/(8x1024x1024) MegaByte/second

[8 bits = 1Byte; 1024 Bytes = 1kiloByte; 1024 kiloByte = 1MegaByte]

                                                            = 150 MBps

c) Considering 15% overhead, the required capacity of the wireless communication channel C = (150 + 150x15% ) = 172.5 MBps = 172.5x1024x1024x8 bits/second = 1447034880 bits/second

Signal to noise ratio in dB = 10log₁₀(S/N) = 30

S/N = 10³ = 1000

Let B be the minimum bandwidth required for this communication.

Using Shannon’s channel capacity criteria for noisy channels,

[putting the previously obtained values of C and S/N]

         

        

d) A practical error correction method is able to achieve 75% of above data rate, i.e. 75% of 150 MBps = 112.5 MBps

Using Nyquist's formula for relation between data rate D, bandwidth B and signal level k,

   ( k is an integer)

Hence, at least 16 signal levels are required to achieve this data rate.