I need matlab code of image denoising by ICA.
Would you please send it to me?
Best regards
Sahar Janii
s.janii[at]stu.nit.ac.ir

ica image denoising matlab code

Abstract

In order to improve the image denoising ability, the wavelet transform (WT) and independent component analysis (ICA) are both introduced into image denoising in this paper. Although these two algorithms have their own advantages in image denoising, they are unable to reduce noises completely, which makes it difficult to achieve ideal effect. Therefore, a new image denoising method is proposed based on the combination of WT with ICA (WT-ICA). For verifying the WT-ICA denoising method, we adopt four image denoising methods for comparison: median filtering (MF), wavelet soft thresholding (WST), ICA, and WT-ICA. From the experimental results, it is shown that WT-ICA can significantly reduce noises and get lower-noise image. Moreover, the average of WT-ICA denoising image’s peak signal to noise ratio (PSNR) is improved by 20.54% compared with noisy image and 11.68% compared with the classical WST denoising image, which demonstrates its advantage. From the performance of texture and edge detection, denoising image by WT-ICA is closer to the original image. Therefore, the new method has its unique advantage in image denoising, which lays a solid foundation for the realization of further image processing task.

1. Introduction

Noise can be interpreted as the factor which hinders the people’s sense organ from understanding and accepting the source information. In the process of the image’s acquisition and transmission, due to pollution by Gaussian noise, the image quality is declined seriously. It would produce unfavorable effects on the following image processing, such as segmentation, compression, and image understanding. The purpose of image denoising is to remove noises, while keeping the main characteristics of information at the same time, such as texture and edge information of image in order to improve the quality of image. Previous studies showed that when the peak signal to noise ratio (PSNR) of a simulation image is lower than 14.2 dB, the probability of false detection of image segmentation is more than 0.5%, and the estimated error of parameters is more than 0.6% [1].

The conventional image denoising methods were based on different statistical characteristics of noise and signal, using the low-pass filters for denoising. In the spatial domain, when the statistics characteristics of noise are unknown, local smoothing operator is selected for denoising. The advantage of this method is that images can be processed in parallel, and less computation time is needed while the drawback is that the selection of window size affects the ability of denoising [2]. If the statistical characteristics of noise are known in the frequency domain, the Wiener filter [3] and least square filter [4] can be used to perform global denoising. But using this method, we need to know the statistical model of noise and signal. As we cannot use simple stochastic process to describe statistical model of image in real applications, the computational cost is relatively high. Low pass filtering method can eliminate the noise effectively, but it can also make the image edge fuzzy at the same time. There are some other denoising methods based on level set, morphological filter, and Markov model [5–7]. To reduce Gaussian noises, many scholars have proposed a series of denoising algorithm, including improved wavelet denoising method [8], improved ICA denoising method [9, 10], improved morphology denoising method [6, 11], method based on neural network [12], and filtering algorithm for improved denoising method [13, 14]. However, the Gaussian noise reduction was still a critical problem, as it was difficult to be removed completely.

In this study, the wavelet transform (WT) and independent component analysis (ICA) are introduced to image denoising, and a kind of WT and ICA-based fusion method for denoising (WT-ICA) is proposed. The new method uses wavelet threshold denoising method to remove Gaussian noise in image; then, it applies ICA to separate the image maximumly into image source signal and noise; finally, it applies wavelet transform to denoise the separated image source signal again. In this way, the new denoising method can get the lower noise image as result. The WC-ICA denoising method achieves the full integration of the advantages of WT and ICA. In the experiments, to obtain different noisy images, we selected three images and added different noises. In order to better verify the denoising ability of the new method, the experiment adopts median filtering (MF), wavelet soft thresholding (WST), ICA, and WT-ICA for comparison. The experimental results indicated that the quality of processed image is greatly improved. The new method can well preserve image texture features and edge details. The PSNR is improved obviously and the obtained low noise image is more conductive for further recognition. In order to explain the effect of noise reduction, we calculate the PSNR and perform edge detection on images, the results of which demonstrate the superiority of the WT-ICA algorithm. The new method has a unique advantage in the denoising Gaussian signals in image, which lays a solid foundation for the further image processing task.

2. Method of WT-ICA Fusion Denoising

Gaussian white noise is considered as the main image noise. The denoising of Gaussian signal is difficult, which has attracted the attention of many scholars. They proposed numerous image denoising methods, some of which have been used to process images and reduce Gaussian noises, and some achievements have been obtained. However, these methods are still unable to reach the ideal denoising effect [15, 16]. In this study, the WT and ICA are introduced into image processing simultaneously. In order to reduce noise pollution of images to the maximum extent, this study tries to combine these two methods together for image denoising.

2.1. Wavelet Denoising

Wavelet transform has good properties of localization both in the time and frequency domains. This characteristic can not only characterize the texture and structure of images at different resolution levels, but also contributes to the edge detection. Therefore, wavelet-based denoising can extract and preserve the edge information, which plays an important role in vision at the same time. It takes the lead in realizing nonlinear transform denoising of image. It is one of the hotspots in image processing field, and more and more new methods are proposed.

All the wavelet denoising methods follow the basic principle: the wavelet coefficients of image source signal and noise have different properties at different scales. By constructing the corresponding evaluation criteria, WT uses mathematical methods to process the corresponding wavelet coefficients of noise signal in the wavelet domain. This study adopts the wavelet threshold denoising method, and the evaluation criterion is the predetermined threshold. That is, we process wavelet coefficients according to a predetermined threshold. If wavelet coefficients are less than a predetermined threshold, these coefficients resulting from the noise thus can be ignored. Otherwise, it is regarded that wavelet coefficients are caused by the image signal source; thus, these coefficients are kept or expanded, and then we reconstruct and restore them. Finally, the low noise image is obtained.

On the one hand, from the mathematical point of view, wavelet denoising belongs to function approximation in the essence. On the other hand, it can seem as a signal filtering problem when it is analyzed from the signal perspective. Therefore, the wavelet denoising is actually an integration of image features extraction and image low-pass filter. Figure 1 is the flow chart of wavelet denoising.

Actual optional PREPROCESSING tools include: Principal Component Analysis (PCA), prewhitening, filtering: High Pass Filtering (HPF), Low Pass Filtering (LPF), Subband filters (Butterworth, Chebyshev, Elliptic) with adjustable order of filters, frequency subbands and the number of subbands).

POSTPROCESSING tools actually includes: Deflation and Reconstruction ("cleaning") of original raw data by removing undesirable components, noise or artifacts.

Moreover, the ICALAB Toolboxes have flexible and extendable structure with the possibility to extend the toolbox by the users by adding their own algorithms.
The algorithms can perform not only ICA ;but also Second Order Statistics Blind Source Separation (BSS) Sparse Component Analysis (SCA), Nonnegative Matrix Factorization (NMF), Smooth Component Analysis (SmoCA), Factor Analysis (FA) and any other possible matrix factorization of the form X=HS+N or Y=WX where H=W+ is a mixing matrix or a matrix of basis vectors.

The ICA/BSS algorithms are pure mathematical formulas, powerful, but rather mechanical procedures: There is not very much left for the user to do after the machinery has been optimally implemented. The successful and efficient use of the ICALAB strongly depends on a priori knowledge, common sense and appropriate use of the preprocessing and postprocessing tools. In other words, it is preprocessing of data and postprocessing of models where expertise is truly needed (see the book).
On the other hand, the assumed linear mixing models must be valid at least approximately and original sources signals should have specified statistical properties.
ICALAB can be useful in the following tasks:

Reduction of redundancy (Chapter 3),
Decomposition of a sequence of images into independent components (Chapters 6-8),
Spatio-temporal decorrelation of correlated signals (Chapter 4),
Extraction and removal of undesirable artifacts and interference by applying deflation (see Chapters 1 and 4),
Removal of noise or "cleaning" the raw sensor data,
Extraction of features and patterns,
Comparison of the performance of various algorithms for Independent Component Analysis (ICA), Blind Source Separation (BSS), Sequential Blind Sources Extraction (BSE) algorithms.
The package contains a collection of algorithms for whitening, robust orthogonalization, ICA, BSS and BSE. The user can easily compare various algorithms for Blind Source Separation (BSS) employing the second order statistics (SOS) and ICA using the higher order statistics (HOS). This package is hence quite versatile and extendable for a user algorithm.

Several benchmarks are included to illustrate the performance of the various algorithms for a selection of synthetic and real world images (see Benchmarks).

Limitation of version 2.0:

The version 2.0 of the package is limited to a maximum of 16 images. In the future, we plan to extend ICALAB for Image Processing for processing up to 256 images, which might be useful for applications such as computer tomography and functional neuroimaging.