2D Orthogonal Locality Preserving Projection for Image Denoising

Abstract

Sparse representations using transform-domain techniques are widely used for better interpretation of the raw data. Orthogonal locality preserving projection (OLPP) is a linear technique that tries to preserve local structure of data in the transform domain as well. Vectorized nature of OLPP requires high-dimensional data to be converted to vector format, hence may lose spatial neighborhood information of raw data. On the other hand, processing 2D data directly, not only preserves spatial information, but also improves the computational efficiency considerably. The 2D OLPP is expected to learn the transformation from 2D data itself. This paper derives mathematical foundation for 2D OLPP. The proposed technique is used for image denoising task. Recent state-of-the-art approaches for image denoising work on two major hypotheses, i.e., non-local self-similarity and sparse linear approximations of the data. Locality preserving nature of the proposed approach automatically takes care of self-similarity present in the image while inferring sparse basis. A global basis is adequate for the entire image. The proposed approach outperforms several state-of-the-art image denoising approaches for gray-scale, color, and texture images.

Comprehensive analysis and evaluation to unsupervised binary hashing method in image similarity measurement

“…To generate the low‐dimensional vector , the concept of the OLPP is used [15–17]. First, the affinity matrix A is constructed.…”

“…Using the orthogonal locality preserving projection (OLPP) [15–17], the proposed unsupervised binary hashing (UBH) method preserves the Euclidean metric and the local structures. To find the optimal projection matrix that preserves structures, the OLPP solves the optimisation problem which is represented by the sum of weighted distances between projected raw feature vectors.…”

A Novel Algorithm based on UBTMF for Colour Pictures

“…Their algorithm was predicated on Chromaticity-Effulgence (CB) colour model which disuniting the colour image into two components: chromaticity and effulgence [30]. Gitam Shikkenawis proposed sparse representations utilizing transform-domain techniques which are widely utilized for better interpretation of the raw data [31]. Igor Djurovi´c analysed that there was a paramount recent advance in filtering of the salt-and-pepper noise for digital images [32].…”

Robust Tensor Decomposition for Image Representation Based on Generalized Correntropy

“…If original samples are given as matrices (2D data), each matrix needs to be transformed into a vector to form a large training matrix. In this way, unfortunately, the underlying spatial (structural) information of the original data is destroyed and thus this matrix-to-vector transformation procedure is not optimal for the extraction of the most representative features [6]- [10]. Moreover, the dimension of the vector space might be very high.…”