Signals, Images and More

Advanced Computational Signal/Image Processing

This course:

www.wavelet-tour.com

sounds videos 3D meshes

→ 25% mathematical theory (filtering, wavelets, regularization, . . . ).

(compression, inpainting, super-resolution, segmentation, . . . ).→ lots of problems

→ needs mathematical modeling and fast processing algorithms.

→ 25% fast numerical algorithms

→ lots of different datas (sounds, images, videos, meshes, . . . ).

→ 50% practical implementation on real applications (Scilab / Matlab).

(wavelet transform, gradient methods, . . . ).

JPEG compression:

JPEG-2000 compression:

→ uses local Fourier transform.

→ blocking artefacts.

→ uses wavelet transform.

→ better compression.

Wavelet CompressionEnter Wavelets…

• Standard 2-D tensor product wavelet transform

Image f JPEG, R = .19bit/pxl JPEG2k, R = .15bit/pxl

JPEG Compression

256x256 pixels, 12,500 total bits, 0.19 bits/pixel

JPEG Compression

256x256 pixels, 12,500 total bits, 0.19 bits/pixel

EZW Compression

256x256 pixels, 9,800 total bits, 0.15 bits/pixel

2D wavelets

Noise in Images

Wavelet thresholdingDenoising using

Inpainting: recovering missing information.

Compressed sensing: designing more efficients sensors.→ use randomized and delocalized measurements.

→ interpolate the image.

Inverse Problems