Efficient Dictionary Learning with Sparseness-Enforcing Projections

TL;DR

This paper introduces EZDL, a fast, simple, and efficient dictionary learning algorithm that enforces sparsity through projections, achieving comparable performance to benchmarks with significantly reduced computational complexity.

Contribution

The paper presents a novel linear-time, constant-space algorithm for sparse dictionary learning based on a new characterization of sparseness projections, enabling rapid and effective image data processing.

Findings

EZDL learns dictionaries approximately 30% faster than existing algorithms.

The learned dictionaries exhibit topographic organization and separability.

EZDL achieves comparable denoising and image reconstruction quality to benchmark methods.

Abstract

Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is enforced to be explicitly sparse with respect to a smooth, normalized sparseness measure. This involves the computation of Euclidean projections onto level sets of the sparseness measure. While previous algorithms for this optimization problem had at least quasi-linear time complexity, here the first algorithm with linear time complexity and constant space complexity is proposed. The key for this is the mathematically rigorous derivation of a characterization of the projection's result based on a soft-shrinkage function. This theory is applied in an original algorithm called Easy Dictionary Learning (EZDL), which learns dictionaries with a simple and fast-to-compute Hebbian-like learning rule. The new algorithm is efficient, expressive and particularly simple to implement. It is demonstrated that despite its simplicity, the proposed learning algorithm is able to generate a rich variety of dictionaries, in particular a topographic organization of atoms or separable atoms. Further, the dictionaries are as expressive as those of benchmark learning algorithms in terms of the reproduction quality on entire images, and result in an equivalent denoising performance. EZDL learns approximately 30 % faster than the already very efficient Online Dictionary Learning algorithm, and is therefore eligible for rapid data set analysis and problems with vast quantities of learning samples.