Denoising multi-view images by soft thresholding: A short-time DFT approach

Abstract

Short-time discrete Fourier transform (ST-DFT) is known as a promising technique for image and video denoising. The seminal work by Saito and Komatsu hypothesized that natural video sequences can be represented by sparse ST-DFT coefficients and noisy video sequences can be denoised on the basis of statistical modeling and shrinkage of the ST-DFT coefficients. Motivated by their theory, we develop an application of ST-DFT for denoising multi-view images. We first show that multi-view images have sparse ST-DFT coefficients as well and then propose a new statistical model, which we call the multi-block Laplacian model, based on the block-wise sparsity of ST-DFT coefficients. We finally utilize this model to carry out denoising by solving a convex optimization problem, referred to as the least absolute shrinkage and selection operator. A closed-form solution can be computed by soft thresholding, and the optimal threshold value is derived by minimizing the error function in the ST-DFT domain. We demonstrate through experiments the effectiveness of our denoising method compared with several previous denoising techniques. Our method implemented in Python language is available from https://github.com/ctsutake/mviden.