Highly Nonlinear Approximations for Sparse Signal Representation


High Quality Sparse Representation of 3D Images

Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using much less elementary components than the number of intensity points in the 3D array. This is achieved by means of a highly redundant dictionary and a dedicated pursuit strategy especially designed for possible implementation in Graphics Processing Unit (GPU) Programming. The benefit of the proposed framework is illustrated in the first instance by demonstrating the gain in dimensionality reduction obtained when approximating true color images as very thin 3D arrays, instead of performing an independent channel by channel approximation. The full power of the approach is further exemplified by producing high quality approximations of hyper-spectral images with a reduction of up to 371 times the number of data points in the representation.

"Sparse Representation of 3D Images for Dimensionality Reduction with High Quality Reconstruction"
by Laura Rebollo-Neira and Daniel Whitehouse

The routines for implementing the methods and reproducing the results of the paper are available here. Note: the file is 1.2 GB because it contains large images.

See below a few examples of approximated images.

Original 24 bpp Image

Image Recovered from a 2.1 bpp file

Original 24 bpp Image

Image Recovered from a 4.1 bpp file

Original 24 bpp Image

Image Recovered from a 4 bpp file