Exercise 6

Topic: Detection theory. Neyman-Pearson test applied on detection of blood vessel in ultrasound color Doppler.

Literature: van Trees:  Detection and estimation.....

We are using the same ultrasound image as in exercise 3  oppg3Data.mat

The file contains a complex demodulated IQ-signal for an image from a linear array probe.

Center frequency 7.5 MHz. It is transmitted 7 pulses for each beam, in total 66 beams. PRF=750MHz.

iq(k,r,b) is the IQ-signal for pulse k, range r, beam b.

We will be using a FIR clutter-filter (filterorder=6) to remove "clutter" from tissue. Then we will get a complex sample x(r,b) from each point in the image which will be used in a likelihood ratio test for blood detection.

A suggested filter:  h=remez(6,[0 .05 .1 .2 .4 1],[0 0 0 0 1 1],[1000 10 1]);

We assume the signal x(r,b) is a complex Gaussian variable (i.e. the real and the imaginary part are uncorrelated Gaussian variables with equal standard deviation).
The signal power is P=E(|x|^2) = N0 outside the blood vessel and P= N0 + Pb inside the blood vessel, where N0 is thermal noise power and Nb is blood signal power.

Make an expression for the probability distribution of x given H0 (outside the blood vessel) and H1 (inside the blood vessel).

Make a likelihood ratio test, and compute ROC for a Neyman-Pearson test (this can be done numerically). Use as an example N0=1 and Pb=3.

Try to estimate N0 and Pb from the example, and find the threshold for Pf=10%.

Use the test to make a binary image. What does Pf and Pm mean in this application?