Learning with few samples

DIP fitting with L2 loss; z is a random image of the same size as x

Before fitting x perfectly, model reconstructs clean image

It is more difficult to fit the noise and corruption

Using Unet architecture (often without skip connections)

Application: Radon transform

+ works well, no trainung data, no domain adaption

- worse result han supervised; bad for low frequency corruption

Given: distribution of noisy imahes for the sample p(y)

With infinite data: average of noise samples is clean sample

Alternative formulation:

1. Train with labeled data with ground truths

2. Pseudo labels for unlabeled data with trained model

3. Retrain with labeled and pseudo labeled data (using weight factor)

4. Iterate over Steps 2 and 3

Train 2 interacting networks for generating pseudo-labels

One evolove slower than the other one

Total loss including consistency loss:

1. For given teacher net, train student net

2. Update teacher nets parameters

Semi supervised loss:

• Similar representations for similar classes

• Enforce representations of close samples to be close

• Closeness by affinity matrix:

Labeled samples: pixels with the same label are close

Unlabeled: pixels sourrounding image patches are similiar

Compact representations can be enforced by minimizing the distance between close samples and max not closed

Closeness in the original space acts as sirrogate label

Final cost function:

Transformation consistency

Final semi-supervised loss function:

Idea: train network with pre-text task only requires images

Finerune network with few labeled samples

Challenge: Define pre-task which learns useful features

Example: rotation angle, intesities, etc.

Surrogate labeling: random transformations of the same image are close

Force close images to be close in representation space

Generating large scale labeled data not feasible

Manual annotations can be costly to obtain; Costly ground truth images, bad aquiring techniques, labeling problems

Goal: being able to work ith few labeled images

Many unlabeled examples: images without labels