图像变换法去噪综述：比较与评价

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本文档《Transform Based Image Denoising: A Review》是一篇综述性的研究文章，主要探讨了图像去噪技术中的变换域方法。随着数字图像处理技术的发展，去除原始图像中的噪声仍然是一个挑战。过去二十年间，研究人员开发了多种噪声减少技术，其中重点介绍了变换域（如Ridgelet Transform、Curvelet Transform）在图像去噪中的应用。首先，作者强调了图像噪声的定义，它指的是图像中随机的亮度或颜色变化，这些变化可能会影响图像的清晰度和细节。噪声可以分为多种类型，如椒盐噪声、高斯噪声等，针对不同类型的噪声，变换域方法提供了有效的处理手段。这些变换，如一般ridgelets和curvelets，能够捕捉到图像的局部特征并分离噪声与信号，从而实现更精确的去噪。文章深入讨论了Empirical Mode Decomposition (EMD) 和 Intrinsic Mode Functions (IMF) 这两种基于经验的方法，它们通过分解图像信号为多个具有内在周期性和趋势的固有模态来识别和移除噪声。同时，作者也探讨了Empirical Ridgelet Transform (ERT) 和 Empirical Curvelet Transform (ECT)，这两种是结合了经验分解和变换理论的优势，旨在进一步提升去噪性能。定量评估是此类研究的关键部分，作者通过计算峰值信噪比（PSNR）来比较不同方法的去噪效果。PSNR是一种常用的评价图像质量的指标，它衡量了重构图像与原始图像之间的差异。通过对比分析，作者旨在揭示各种变换域去噪技术的优势和局限性，为实际应用提供指导。这篇论文为读者提供了对变换域图像去噪技术的全面了解，包括各种方法的工作原理、优缺点以及在实际应用中的性能对比。对于那些在图像处理领域，特别是噪声抑制技术感兴趣的研究者和工程师来说，这是一份宝贵的参考资料。

168

Transform Based Image Denoising:A Review

Nidhi Soni

Department of E&C

Samrat Ashok Technological Institute, Vidisha

soni.nidhi0108@gmail.com

K.G. Kirar

Department of E&I

Samrat Ashok Technological Institute, Vidisha

kg.kirar@gmail.com

__________________________________________________________________________________________

Abstract – The challenge to remove noise from

original image still exists. Over the past two decades,

different kinds of noise reduction techniques have

been developed. This paper reviews the transform

based denoising techniques and performs their

comparative study. Here we put results of different

approaches including general ridgelets and curvelets,

Empirical Mode Decomposition and Empirical

ridgelets and curvelets. A quantitative measure of

comparisons is presented in terms of PSNR.

Keywords – Ridgelet Transform, Curvelet Transform,

Empirical Mode Decomposition, Intrinsic Mode

Functions, Empirical Ridgelet Transform, Empirical

Curvelet Transform

I. INTRODUCTION

Image noise is the random variation of brightness

or color information in images, which alters the

original information of an image. Image denoising

is done to remove this alteration and restore the

original image. The ridgelet transform discussed in

section II was introduced by Candes and Donoho

[1, 2, 3] and was one of the first directional 2D

wavelet type transform. It considers the usual

wavelet transform on a collection of a 1D signal.

While in the empirical ridgelet transform

elaborated in section IV, we use empirical wavelet

transform instead of standard wavelet transform [4]

The curvelet transform was introduced by Candes

et al. [5, 6, 7]. Curvelet transform can provide a

stable, efficient, and near-optimal representation of

smooth objects discontinuities along smooth

curves. It is a multiscale transform which is more

adapted to the image processing after wavelet

transform. Empirical mode decomposition(EMD)

concept that utilizes the Hilbert–Huang transform

(HHT) is expanded into two dimensions for the

images[8]. It provides a tool for image processing,

further discussed in Section III. The conclusion and

results are discussed in section V and section VI

respectively.

II. RIDGELETS AND CURVELETS

The ridgelet and curvelet transforms were

developed to overcome the limitations of the

wavelet transform. The limitation arises from the

fact that along the important edges in the image, the

two-dimensional (2-D) wavelet transform contains

large wavelet coefficients. That means many

wavelet coefficients are required to reconstruct the

edges in an image properly. Denoising also

becomes challenging with so many coefficients to

estimate. So, to represent smooth function and

edges with a few nonzero coefficients accurately,

the ridgelet transform and curvelet transform were

developed.

Consider the usual wavelet transform on a

collection of a 1D signal. This 1D signal collection

is generated by an inverse 1D Fast Fourier

Transform (FFT) of the 1D spectrum problem

extracted from the 2D FFT of input image along

lines going through the origin and with angle Ɵ. By

using our notations, the classical ridgelet transform

can be written, 0 < n < N (where n = 0 corresponds

to the approximation sub band) [4],

n, θ, t)= ѡ

1,t

(Ғ*

1,|ω|

( Ғ

(f)( θ,|ω|))) (2.1)

And it’s inverse

f(x)= Ғ*

(Ғ

1,t

(ѡ*

1,t

(ѡ

)) (2.2)

Proceeding International conference on Recent Innovations is Signal Processing and Embedded Systems (RISE-2017) 27-29 October,2017

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