Module 4: Interferometry
  Lecture 24: Iterative algorithms
 

Sensitivity to Noise in projection Data

In measurements involving commercial grade optical components and recording and digitizing elements, the projection data is invariably superimposed with noise. Software operations such as interpolation and image processing can also contribute to errors in the projection data. Experience of the authors with interferometric experiments shows that the RMS noise level is around [78].

The performance of the three proposed algorithms has been compared with noisy projection data as the input. A noise level has been adopted for all calculations. The noise pattern has been generated using a random number generator, with a uniform probability density function. Results have been presented for 2 and 4 projections corresponding to view angles of respectively. The initial guess for reconstruction with 2 projections is simply a constant; for 4 projections the result obtained with 2 projections has been used as the initial guess.

Results with 2 projections show that all three algorithms reproduce qualitatively the temperature field of Figure 2. However quantitative differences are to be seen. The noise level in the reconstructed field is found to be slightly higher than that in the projection data. The magnitude of the three different errors and the distribution of the fractional error over the fluid domain are presented in Table 14. All the three algorithms are practically equivalent in terms of errors, though AVMART2 is seen to be marginally better from the error point of view. However the CPU time of AVMART1 is minimum. It is to be noted that noise (in terms of ) in the projection data has been amplified during the reconstruction process This is in contrast to noise in the initial guess. Where iterations tend to diminish errors in the converged field.

Table 14: Comparision of the AVMART Algorithms: Noise in Projection Data, Two-View Reconstruction

Quantity
AVMART1
AVMART2
AVMART3
4.452
4.449
4.450
1.08
1.08
1.08
6.37
6.36
6.37
Number of Points (%) having error int he range
>95
0.004
0.004
0.004
75-95
0.222
0.200
0.222
50-75
4.400
4.387
4.400
Inerations
9
12
14
CPU,sec
30.5
40.9
47.8