Horseshoes in Wavelet Domains

Music City Center 

In recent years, horseshoe priors have gained prominence in Bayesian statistics for their remarkable ability to induce sparsity in high-dimensional data. This talk explores the application of traditional and new horseshoe priors for shrinkage in wavelet domains, a powerful framework for function and image denoising. We begin by reviewing the theoretical underpinnings of horseshoe priors and their advantages over traditional shrinkage methods, particularly in terms of adaptivity and simplicity in estimation in the presence of noise.
Next, we delve into the integration of horseshoe priors with wavelet transforms, illustrating how this combination enhances sparsity and leads to robust denoising and compression techniques. Horseshoe priors also lead to "second posterior mode wavelet shrinkage (SPMWS)," an efficient thresholding technique. Through several simulations and real-world examples, we demonstrate the effectiveness of these techniques in recovering signals from their sparse representations and highlight their potential in various applications.

Wavelet transform

Horseshoe priors

Bayesian Statistics

Wavelet shrinkage