G-SVD驱动的逆半色调技术提升图像重建质量

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本文主要探讨了"分组奇异值分解的反向半色调"（Inverse Halftoning with Grouping Singular Value Decomposition，简称G-SVD）这一新颖的图像处理技术。在传统的图像处理领域，尤其是从二值半色调图像（bi-level halftone image）恢复连续色调图像（continuous-tone image）的过程中，由于数据冗余度低，重建过程极其复杂，往往导致重构结果的视觉质量受限。分组奇异值分解（G-SVD）的核心思想是通过将相似的图像块进行聚类或分组，这样可以有效地组织和利用输入数据中的结构信息。这种方法旨在找到输入空间中数据密度较高的低维特征表示，这些特征区域通常包含了图像中的关键内容。通过这种方式，G-SVD能够减少噪声的影响，同时增强非局部图像区域间的相似性，因为相似的像素在低维特征空间中更可能聚集。在反向半色调的实现中，作者引入了由G-SVD公式化的一系列约束条件。这些约束有助于区分图像中的噪声成分和有意义的图像内容，使得在逆半色调重建过程中，能够更精确地还原细节和纹理。通过这种方法，G-SVD不仅提升了图像重建的质量，而且在视觉效果上超越了现有的相关技术。实验部分展示了G-SVD在实际应用中的优势，通过客观和主观评估指标，如PSNR（Peak Signal-to-Noise Ratio，信噪比）、SSIM（Structural Similarity Index，结构相似性指数）等，证明了新方法在重建灰度图像时能提供显著的提升，无论是从视觉感知还是量化评估上，都展现出更高的性能。总结来说，分组奇异值分解的反向半色调算法为解决图像处理中的逆半色调问题提供了一种创新且有效的解决方案，通过利用数据分组和低维特征表示，成功改善了图像质量，有望在图像复原、图像分析和图像压缩等领域发挥重要作用。

INVERSE HALFTONING WITH GROUPING SINGULAR VALUE DECOMPOSITION

Jun Yang

1,2

Jun Guo

Hongyang Chao

3,∗

School of Information Science and Technology, Sun Yat-sen University, Guangzhou, P.R. China

SYSU-CMU Shunde International Joint Research Institute, P.R. China

School of Software, Sun Yat-sen University, Guangzhou, P.R. China

ABSTRACT

The objective of inverse halftoning refers to reconstruct a

high quality gray scale image from bi-level halftone im-

age. However, reconstructing continuous-tone images from

their halftoned versions is highly underdetermined, making

this technique very difﬁcult. In this paper, we present the

Grouping Singular Value Decomposition (G-SVD), a novel

approach which ﬁrst groups similar image patches as input

and then characterizes lower-dimensional regions in input s-

pace where the data density is peaked. By adding a constraint

formulated via G-SVD into inverse halftoning, noises are

separated from meaningful contents and similarity of nonlo-

cal image patches is promoted. Our experiments shown that

the proposed approach could improve the visual quality of

reconstructed results and outperformed the state of the arts in

terms of both objective and subjective measurements.

Index Terms— inverse halftoning, grouping singular val-

ue decomposition (G-SVD), nonlocal similarity

1. INTRODUCTION

Halftoning provides the ability of representing an image with

only one color through the use of ink dots, and is thus widely

used in today’s publishing applications, such as newspapers,

books, magazines, etc. [1, 2]. Halftone images are typically d-

ifﬁcult to manipulate. Many halftone image processing, such

as scaling, compression, and enhancement could cause severe

image degradation [3]. To enable these operations, gray im-

ages need to be reconstructed from halftones through inverse

halftoning. For scanning printed (halftone) images inverse

halftoning is also needed to reduce Moire effects.

Therefore, as shown in Fig. 1, halftoned images are of-

ten inverse halftoned. Considering that inverse halftoning is

an operation mapping {0, 1}

H×W

onto R

H×W

(H / W is

the image height / width), this technique apparently belongs

to the class of ill-posed inverse problems and is rather chal-

lenging. In the last two decades, lots of inverse halftoning

This work was partially supported by NSF of China under Grant

61173081 and Guangdong Natural Science Foundation, China, under Grant

S2011020001215.

∗

Corresponding author: Hongyang Chao (isschhy@mail.sysu.edu.cn)

Fig. 1. An illustration of inverse halftoning: original image

(left), halftoned (center) and inverse halftoned version (right).

algorithms were developed to exploit local smoothness of im-

ages and have achieved good results, including tree-structured

vector quantization [4], convex set projection [5], iterative s-

tatistical smoothing [6], nonlinear permutation ﬁltering [7],

anisotropic ﬁltering [8], shearlet representation [9], Bayesian

approaches [10, 11], look-up-table (LUT) based approach-

es [12] and wavelet-based approaches [13, 14, 15]. However,

while local smoothness was preserved, these algorithms usu-

ally produced blurry results, and thus had shortcomings in

keeping edges and textures. Targeting at this problem, the re-

cently proposed BM3D-based approach [16] added a regular-

ization term of nonlocal similarity, and achieved the state-of-

the-art performance. However, there is still one main problem

to restrict its performance. The BM3D-based approach relied

on a sophisticated deterministic annealing optimization [17],

which requires to denoise reconstructed images in each itera-

tion. Hence, its output usually consists of visible artifacts.

To resolve this issue, while minimizing residual errors be-

tween an input halftoned image and the re-halftoned version

of its reconstructed image so as to maintain local smooth-

ness, we plug in a novel constraint expressed via the pro-

posed Grouping Singular Value Decomposition (G-SVD) ap-

proach to promote self-similarity of nonlocal image patches.

By grouping similar nonlocal image patches and then limiting

the minimal nonzero singular value of each group to be a large

number, our G-SVD constraint can capture a low-dimensional

manifold from each group. As a result, saliency patterns with-

in a group, e.g., the outline of a human’s face, can be dis-

covered, while at the same time artifacts are well separat-

ed, which in turn enhances the similarity of nonlocal patches

within this group. To optimize our whole framework, we al-

so leverage G-SVD to build an iterative projection method, in

order to ensure the lower bound of singular values of groups.

Extensive experiments show the superior performance of our

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G-SVD驱动的逆半色调技术提升图像重建质量

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