Cross-scale predictive dictionaries

TL;DR

This paper introduces a multi-scale predictive dictionary model that accelerates sparse approximation for visual signals, achieving 10-60 times faster solutions with minimal accuracy loss in inverse problems.

Contribution

It proposes a novel cross-scale structure for sparse representations that significantly speeds up inverse problem solutions for images, videos, and light fields.

Findings

Achieves 10-60x speedup in sparse approximation tasks.

Maintains high accuracy with minimal loss in inverse problem solutions.

Effective across various visual signal modalities.

Abstract

Sparse representations using data dictionaries provide an efficient model particularly for signals that do not enjoy alternate analytic sparsifying transformations. However, solving inverse problems with sparsifying dictionaries can be computationally expensive, especially when the dictionary under consideration has a large number of atoms. In this paper, we incorporate additional structure on to dictionary-based sparse representations for visual signals to enable speedups when solving sparse approximation problems. The specific structure that we endow onto sparse models is that of a multi-scale modeling where the sparse representation at each scale is constrained by the sparse representation at coarser scales. We show that this cross-scale predictive model delivers significant speedups, often in the range of 10-60$\times$, with little loss in accuracy for linear inverse problems associated with images, videos, and light fields.