Any form of signal processing having image as an input and output (or a set of characteristics or parameters of image) is called image processing. In image processing we work in two domains i.e., spatial domain and frequency domain. Spatial domain refers to the image plane itself, and image processing method in this category are based on direct manipulation of pixels in an image and coming to frequency domain it is the analysis of mathematical functions or signals with respect to frequency rather than time.
Image Denoising : Overview
The search for efficient image denoising methods still is a valid challenge, at the crossing of functional analysis and statistics. Image denoising refers to the recovery of a digital image that has been contaminated by noise. The presence of noise in images is unavoidable. It may be introduced during image formation, recording or transmission phase. Further processing of the image often requires that the noise must be removed or at least reduced. Even a small amount of noise is harmful when high accuracy is required. The noise can be of different types. The most popular ones are additive white Gaussian noise (AWGN).
An image denoising procedure takes a noisy image as input and outputs an image where the noise has been reduced. Numerous and diverse approaches exist: Some selectively smooth parts of a noisy image. Other methods rely on the careful shrinkage of wavelet coefficients. A conceptually similar approach is to denoise image patches by trying to approximate noisy patches using a sparse linear combination of elements of a learned dictionary. Learning a dictionary is sometimes accomplished through learning on a noise-free dataset. Other methods also learn a global image prior on a noise-free dataset, for instance. An image is often corrupted by noise in its acquisition and transmission. Image denoising is used to remove the additive noise while retaining as much as possible the important signal features. Generally, data sets collected by image sensors are contaminated by noise. Imperfect instruments, problems with data acquisition process, and interfering natural phenomena can all corrupt the data of interest. Thus noise reduction is an important technology in Image Analysis and the first step to be taken before images are analyzed. Therefore, Image Denoising techniques are necessary to prevent this type of corruption from digital images.
Technique of Image Denoising
Various image denoising techniques have been developed so far and their application depends upon the type of image and noise present in the image. Image denoising is classified in two categories:
Spatial domain filtering: This is the traditional way to remove the noise from the digital images to employ the spatial filters. Spatial domain filtering is further classified into linear filters and nonlinear filters.
Linear Filters: A mean filter is the optimal linear for Gaussian noise in the sense of mean square error. Linear filters tend to blur sharp edges, destroy lines and other fine details of image. It includes Mean filter and Wiener filter.
Transform domain filtering: The transform domain filtering can be subdivided into data adaptive and non-adaptive filters. Transform domain mainly includes wavelet based filtering techniques.
Wavelet Transform: Wavelet transform is a mathematical function that analyzes the data according to scale or resolution. Noise reduction using wavelets is performed by first decomposing the noisy image into wavelet coefficients i.e. approximation and detail coefficients. Then, by selecting a proper Thresholding value the detail coefficients are modified based on the Thresholding function. Finally, the reconstructed image is obtained by applying the inverse wavelet transform on modified coefficients. Basic procedure for all Thresholding method is:
- Calculate DWT if the Image.
- Threshold the wavelet components.
- Compute IDWT to obtain denoised estimate.
There are two Thresholding functions frequently used i.e. Hard Threshold, Soft threshold. Hard Thresholding function keeps the input if it is larger than the threshold; otherwise, it is set to zero. Soft-Thresholding function takes the argument and shrinks it toward zero by the threshold. Soft-Thresholding rule is chosen over hard Thresholding, for the soft-Thresholding method yields more visually pleasant images over hard Thresholding. A result may still be noisy. Large threshold alternatively, produces signal with large number of zero coefficients. This leads to a smooth signal. So much attention must be paid to select optimal threshold.
Example of Image Denoising
 Burger, Harold C., Christian J. Schuler, and Stefan Harmeling, “Image denoising: Can plain neural networks compete with BM3D?” In Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on, pp. 2392-2399.
 Alisha P B and Gnana Sheela K, “Image Denoising Techniques-An Overview”, IOSR Journal of Electronics and Communication Engineering (IOSR-JECE), Volume 11, Issue 1, Ver. I (Jan. – Feb .2016), PP 78-84
 C. Kervrann and J. Boulanger, “Patch-based Image Denoising”, available online at: https://www.irisa.fr/vista/Themes/Demos/Debruitage/ImageDenoising.html