Computationally Efficient Truncated Nuclear Norm Minimization for High Dynamic Range Imaging

Abstract

Matrix completion is a rank minimization problem to recover a low-rank data matrix from a small subset of its entries. Since the matrix rank is nonconvex and discrete, many existing approaches approximate the matrix rank as the nuclear norm. However, the truncated nuclear norm is known to be a better approximation to the matrix rank than the nuclear norm, exploiting a priori target rank information about the problem in rank minimization. In this paper, we propose a computationally efficient truncated nuclear norm minimization algorithm for matrix completion, which we call TNNM-ALM. We reformulate the original optimization problem by introducing slack variables and considering noise in the observation. The central contribution of this paper is to solve it efficiently via the augmented Lagrange multiplier (ALM) method, where the optimization variables are updated by closed-form solutions. We apply the proposed TNNM-ALM algorithm to ghost-free high dynamic range imaging by exploiting the low-rank structure of irradiance maps from low dynamic range images. Experimental results on both synthetic and real visual data show that the proposed algorithm achieves significantly lower reconstruction errors and superior robustness against noise than the conventional approaches, while providing substantial improvement in speed, thereby applicable to a wide range of imaging applications.

High Dynamic Range Imaging Based on Bidirectional Structural Similarities and Weighted Low-Rank Matrix Completion

“…e estimated low-rank matrix is the background irradiance map. Lee and Lam [27] employed truncated nuclear norm minimization to accelerate the algorithm. However, their performance relies highly on the selection of the missing regions.…”

“…However, their performance relies highly on the selection of the missing regions. In [26,27], part of missing regions requires user specification. When the scene is complex, it is hard for the user to do so.…”

High Dynamic Range Light Fields via Weighted Low Rank Approximation

“…Regarding HDR images, their acquisition generally involves taking several pictures of the scene at different exposures. A large panel of methods have been developed for merging the captured images into an HDR one, including patch-based methods [1][2][3], Low Rank Matrix Completion (LRMC) [4][5][6][7], and more recently deep learning [8]. A comprehensive review of the subject is provided in [9].…”

“…We show that our non-binary approach better handles the transition between the saturated and non-saturated areas. Furthermore, unlike the the Truncated Nuclear Norm minimization previously used in several HDR imaging methods [4][5][6][7], our rank minimization successfully applies to light fields where the rank is expected to be higher than 1 because of the parallax. We finally show the advantage of processing the different viewpoints simultaneously.…”

Motion Capture Data Completion via Truncated Nuclear Norm Regularization

“…Till now, TrNN has been successfully applied in many fields, such as image inpainting [20], [21], [22], background subtraction [19], multi-class classification [23], photometric stereo [24], [25] and high dynamic range imaging [26], [27]. To the best of our knowledge, this is the first time to use TrNN tackling the mocap data completion problem.…”