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) I now realized that the quantitative metrics should be normalized by the number of bubbles in the patch (image) that you are processing, so that what you report is the average metric per bubble.

2) I am not clear as to what f you are using for the quantitative metrics, as you are using the same symbol as the f used in computing the loss in training the NN. Please use f_0 for the the one used for the quantitative metrics, and f for the one used for training, and report both. Also report whether each of them is circular in pixel of physical coordinates.

3) For each such set of experiments, it would be good to summarize the results in a table, giving the parameters used (including number of epochs used and batch size – in a caption if same for all experiments), the values of the quantitative metrics, and the % gap between the loss on the training and on the validation data, at the end of training.

1) Done.

2) Done.

3) Here is the summary: https://ufuksoylu.web.illinois.edu/2019/07/25/summary/