Fast Sublinear Sparse Representation using Shallow Tree Matching Pursuit

TL;DR

This paper introduces a fast, hierarchical tree-based method for sparse representation that significantly reduces computation time in image processing tasks while maintaining high accuracy.

Contribution

It presents a novel shallow tree matching pursuit framework that accelerates sparse approximation in over-complete dictionaries for imaging applications.

Findings

Achieves 100-1000x speedup in image denoising and super-resolution.

Maintains less than 1dB loss in accuracy compared to traditional methods.

Effective in compressive sensing and light-field analysis.

Abstract

Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately, the applicability of such methods is severely hampered by the computational burden of sparse approximation: these algorithms are linear or super-linear in both the data dimensionality and size of the dictionary. We propose a framework for learning the hierarchical structure of over-complete dictionaries that enables fast computation of sparse representations. Our method builds on tree-based strategies for nearest neighbor matching, and presents domain-specific enhancements that are highly efficient for the analysis of image patches. Contrary to most popular methods for building spatial data structures, out methods rely on shallow, balanced trees with relatively few layers. We show an extensive array of experiments on several applications such as image denoising/superresolution, compressive video/light-field sensing where we practically achieve 100-1000x speedup (with a less than 1dB loss in accuracy).