# ULM Through DL 9(Circular Kernel in Physical Dimensions)

Up to this point, we have used circular blur kernel f in pixel coordinates. In this set of experiments, we have used circular blur kernel in physical coordinates. This blog is continuation of previous blogs. Please see the other blogs to learn the experiment procedure.

These results are for far field region. Patches are coming from far field region as in the previous blog.

Note: Best and Worst cases are chosen by comparing the average bubble error in a patch.

Quantitative Metrics: In order to compare success of different experiments, we decide the use the followings:

Quantitative Metric1 = $L1Loss(z**f_0 – x**f_0)$

Quantitative Metric2 = $MSELossLoss(z**f_0 – x**f_0)$

where f_0 is a gaussian kernel with sigma =1.

Note: Both f and f_0 are in physical coordinates.

Experiment 1: learning rate=1e-5, sigma of kernel f=1, regularizer parameter=0.01

Average quantitative metric1 is 21.066962

Average metric1 per bubble is 0.829031

Average quantitative metric2 is 0.805354

Average metric2 per bubble is 0.031346

Worst Case: Center Location(x,z) = 29.61 mm and 48.80 mm , Average Metric1 per bubble: 1.95, Average Metric2 per bubble: 0.133

Best Case: Center Location(x,z) = 17.27 mm and 48.31 mm , Average Metric1 per bubble: 0.3797, Average Metric2 per bubble:0.00542

Experiment 2: learning rate=1e-5, sigma of kernel f=1, regularizer parameter=0.005

Average quantitative metric1 is 21.959468

Average metric1 per bubble is 0.863606

Average quantitative metric2 is 0.812720

Average metric2 per bubble is 0.031575

Worst Case: Center Location(x,z) = 32.07mm and 48.80mm , Average Metric1 per bubble: 1.7694, Average Metric2 per bubble: 0.12264

Best Case: Center Location(x,z) = 19.75mm and 47.32mm , Average Metric1 per bubble: 0.4744, Average Metric2 per bubble: 0.008265

Experiment 3: learning rate=1e-5, sigma of kernel f=1.5, regularizer parameter=0.01

Average quantitative metric1 is 21.031181

Average metric1 per bubble is 0.827787

Average quantitative metric2 is 0.779206

Average metric2 per bubble is 0.030392

Worst Case: Center Location(x,z) = 33.30mm and 48.80mm , Average Metric1 per bubble: 1.828, Average Metric2 per bubble: 0.106

Best Case: Center Location(x,z) = 13.59mm and 36.98mm , Average Metric1 per bubble: 0.514, Average Metric2 per bubble: 0.0099

Experiment 4: learning rate=1e-5, sigma of kernel f=1.5, regularizer parameter=0.005

Average quantitative metric1 is 20.906547

Average metric1 per bubble is 0.823864

Average quantitative metric2 is 0.718547

Average metric2 per bubble is 0.028081

Worst Case: Center Location(x,z) = 29.61mm and 48.80mm , Average Metric1 per bubble: 1.678, Average Metric2 per bubble: 0.1032

Best Case: Center Location(x,z) = 16.05mm and 43.38mm , Average Metric1 per bubble: 0.518, Average Metric2 per bubble: 0.0088

Experiment 5: learning rate=1e-5, sigma of kernel f=2, regularizer parameter=0.01

Average quantitative metric1 is 22.376564

Average metric1 per bubble is 0.881055

Average quantitative metric2 is 0.872184

Average metric2 per bubble is 0.034107

Worst Case: Center Location(x,z) = 33.30mm and 48.80mm , Average Metric1 per bubble: 1.7376, Average Metric2 per bubble: 0.1031

Best Case: Center Location(x,z) = 25.91mm and 45.85mm , Average Metric1 per bubble: 0.606, Average Metric2 per bubble: 0.015455

Experiment 6: learning rate=1e-5, sigma of kernel f=2, regularizer parameter=0.005

Average quantitative metric1 is 23.040157

Average metric1 per bubble is 0.907826

Average quantitative metric2 is 0.863941

Average metric2 per bubble is 0.033746

Worst Case: Center Location(x,z) = 29.61 mm and 48.80 mm , Average Metric1 per bubble: 1.6995, Average Metric2 per bubble: 0.104

Best Case: Center Location(x,z) = 8.66mm and 39.44mm , Average Metric1 per bubble: 0.590, Average Metric2 per bubble: 0.01337 1. Yoram says: