MCA Experiments

This page presents several numerical experiments using the Morphological Component Analysis framework:

Image Decomposition:

Texture Separation:

Inpainting:


Image Decomposition

Separation of lines and gaussians

synt synt0p5
Left, simulated image containing lines, line segments, and gaussians. Right, simulated noisy image (sigma =0.5).

synt_atrou synt_cur
Left, reconstructed image from the wavelet component, and right, reconstructed image from the curvelet component.

synt_filter synt_resi
Left, addition of the two components and residual (difference betweem the noiy data minus the addition of the two components).


Gravitational arc A370 (HST data)

 
Left,A370 HST image and right, reconstruction from the wavelet component.

 
Left, reconstruction from the ridgelet component + the curvelet component, and right, reconstruction from the three components.


Infrared data of the galaxy SBS 0335-052 obtained with GEMINI telescope.

A residual stripping remains after calibration, and the galaxy is not detected by standard methods because of this calibration problem. We decomposed the data onto three bases (wavelets, ridgelets, and curvelets). Ridgelets and curvelets capture the anisotropic information (mainly calibration artifacts), while the wavelets capture the isotropic information (our galaxy).


Texture Separation

We present here some experiments relative the texture separation using MCA.

Boy image: decomposition on the curvelet transform + DCT

  Left, original image; middle, piecewise smooth content part and right, texture part. The addition of the texture part and the piecewise smooth part reproduces the original image.


Application to edge detection

 
Left, Canny edge detection on previous original image and right, Canny edge detection on the piecewise smooth part.


Barbara image: decomposition on the curvelet transform + DCT

  Left, original image; middle, piecewise smooth content part and right, texture part. The addition of the texture part and the piecewise smooth part reproduces the original image.

  Left, original image; middle, piecewise smooth content part and right, texture part. The addition of the texture part and the piecewise smooth part reproduces the original image.


Boy image + Noise: decomposition on the curvelet transform + DCT

 
 

Upper, left original image + noise and right, piecewise smooth content part. Bottom, left texture part and right, residual part. Residual + texture part + piecewise smooth content part = input data.