Read -- Deep Image Prior

Deep convolutional networks <—> DIP
DIP:

• the structure of a generator network is sufficient to capture a great deal of low-level image statistics $prior$ to any learning.
• a randomly initialized neural network can be used as a handcrafted prior
• can be used to invert deep neural representations to diagnose them

Inpainting

a binary mask : $m\in{0,1}^{H\times W}$

• $m_{i, j}=0$ means this is a missing pixel.
• $m_{i, j}=1$ means on position ${i, j}$ pixel is observed.

$\odot$: Hadamard product
$E(x; x_0)$ : the pixel difference between visible pixels

Convolutional Sparse coding (CSC):
represent a signal (such as image or an audio waveform) as
a sum of convolutions between

• a small set of learned filters (the “dictionary”) and
• corresponding sparse activation maps

• Filters ${d_k}$—the small weight matrices that define what patterns to look for, and

• Activation maps ${z_k}$—where and how strongly each filter occurs in the image.

• The reconstruction $\sum_k d_k * z_k$ adds up each filter’s contribution across the image.