Dictionary Pair Learning on Grassmann Manifolds for Image Denoising

Abstract

Abstract-Image denoising is a fundamental problem in computer vision and image processing that holds considerable practical importance for real-world applications. The traditional patch-based and sparse coding-driven image denoising methods convert two-dimensional image patches into one-dimensional vectors for further processing. Thus, these methods inevitably break down the inherent two-dimensional geometric structure of natural images. To overcome this limitation pertaining to previous image denoising methods, we propose a two-dimensional image denoising model, namely, the Dictionary Pair Learning (DPL) model, and we design a corresponding algorithm called the Dictionary Pair Learning on the Grassmann-manifold (DPLG) algorithm. The DPLG algorithm first learns an initial dictionary pair (i.e., the left and right dictionaries) by employing a subspace partition technique on the Grassmann manifold, wherein the refined dictionary pair is obtained through a sub-dictionary pair merging. The DPLG obtains a sparse representation by encoding each image patch only with the selected sub-dictionary pair. The non-zero elements of the sparse representation are further smoothed by the graph Laplacian operator to remove noise. Consequently, the DPLG algorithm not only preserves the inherent two-dimensional geometric structure of natural images but also performs manifold smoothing in the two-dimensional sparse coding space. We demonstrate that the DPLG algorithm also improves the SSIM values of the perceptual visual quality for denoised images using experimental evaluations on the benchmark images and Berkeley segmentation datasets. Moreover, the DPLG also produces the competitive PSNR values from popular image denoising algorithms.

A Fast Dictionary Learning Algorithm for Image Denoising

“…The main difference among most dictionary learning algorithms, such as K-SVD algorithm [8], the Dictionary Pair Learning on the Grassmann-manifold algorithm (DPLG) [9] and first dictionary learning (FDL) [10], is the way of updating the dictionary. However, K-SVD algorithm is expensive.…”

“…To overcome these limitation, other methods for dictionary learning came up to replace the K-SVD. For example, Liu et al [10] and Zeng et al [11]. Zeng et al in [11] proposed a dictionary pair learning model (DPL model) for image denosing and designed a corresponding algorithm, called the DPLG algorithm.…”

“…For example, Liu et al [10] and Zeng et al [11]. Zeng et al in [11] proposed a dictionary pair learning model (DPL model) for image denosing and designed a corresponding algorithm, called the DPLG algorithm. This algorithm learned an initial dictionary pair by the Top-bottom Two-dimensional Subspace Partition algorithm (TTSP algorithm).…”

“…Motivated by ideas in [10] and [11], we propose a fast dictionary learning algorithm for image denosing. Our method is also a two-stage approach that includes dictionary learning stage and sparse coding stage, in which dictionary learning stage is different from the TTSP algorithm in [11] and sparse coding stage is similar to the method in [12] by adding the intrinsic geometric structure of the data through a graph regularized and using the learned dictionary to provide a sparse representation of data patches.…”

Matrix-value Linear Regression for Image Denoising

“…Moreover, vectorization tends to result in the overfitting problem because the dimension of the vectorized images (or image patches) may be larger than that of the sample number. To avoid these defects, some works such as [4,5] have made some attempts at directly using the original image (or image patches) matrices for image denoising.…”