Sparse Representation of 3D Images for Piecewise Dimensionality Reduction with High Quality Reconstruction

TL;DR

This paper introduces a sparse representation method for 3D images that achieves high-quality approximations with significant data reduction, especially effective for hyper-spectral images, using a specialized dictionary and pursuit strategy.

Contribution

It presents a novel sparse representation framework for 3D images that enhances dimensionality reduction and reconstruction quality compared to traditional methods.

Findings

Achieves up to 371-fold data reduction in hyper-spectral images.

Demonstrates superior dimensionality reduction when approximating 3D images as a whole.

Provides high-quality image approximations with fewer elementary components.

Abstract

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 fewer 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 low memory requirements. 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.