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1.1 Digital Image:

An image is defined as artifact or visual representation which is recordedby visual perceptions and then further digitized to convert it in the form which can be stored in the computer memory or some type of storage media such as hard disk or it is said as picture stored in electronic form is known as image. In computer digitization procedure can be done by scanner or by video camera which is connected to frame grabber board. After the image has been digitized it can further operated by various image processing operations.Once digitized an image various operations can be applied for improving the quality and removing the blurredness. These are unwanted particles or electrical signals in image which degrades its quality which is known as noise. Noise is integrated in the images during acquisition, transmission or retrieval of images from storage media 

Appearance of noise in images is in form of dots which can be spotted in a photograph, when image is captured in low lightning conditions. Appearance of dots is due to the real signals getting corrupted by noise (unwanted signals). On television screens, random black and white snow-like patterns can be seen on loss of reception. Both Videos and images noise corrupts. So the main purpose of denoising is to remove such type of noise.A noisy image is not pleasant to view so Image denoising is needed. With the noise, some fine details in the image may be confused. To work effectively many image-processing algorithms such as pattern recognition need a clean image.Noise samples like Random and uncorrelated are not compressible. In image and video processing such concerns underline the importance of denoising. 

1.2 Denoising

Image denoising is an essential task in image processing, both as a component in other processes and as a process itself.  Various Methods are there todenoise the image. The main properties of a good image Denoising model are that it will preserve edges while removing noise. Linear models have been used traditionally. With the noisy image as input-data, i.e. a linear, 2nd order PDE-model. The most common approach is to solving the heat equation or use a Gaussian filter.This kind of Denoising is adequate.The advantage of linear noise removal models is the speed. But a linear model is having some drawbacks that they are not able to preserve edges in a good manner: edges, which are recognized as discontinuities in the image, are smeared out. Nonlinear models on the other hand nonlinear models can handle edges in a much better way than linear models. Total Variation (TV)-filter is the one popular model for nonlinear image Denoising,Total Variation Filter will preserve the edges in very good manner ,but in input image smoothly varying regions are transformed into piecewise constant regions in the output image  using the TV-filter as a denoiser leads to solving a 2nd order nonlinear PDE. Since smooth regions are transformed into piecewise constant regions when using the TV-filter, it is desirable to create a model for which smoothly varying regions are transformed into smoothly varying regions, and yet the edges are preserved. This can be done for instance by solving a 4th order PDE instead of the 2nd order PDE from the TV-filter. This 4th order filter produces much better results in smooth regions, and still preserves edges in a very good way.

Another method is to combine a 4th order and 2nd order approach. by the 4th order scheme smooth regions are filtered, by a 2nd order scheme while edges are filtered. one has to construct a weight function. To choose in which areas of the image each of the models are to be used.


Noise is the one of the major problem in each imaging system.Noise may be defined as an unwanted data which may reduce the contrast deteriorating the shape or size of objects in an image and blurring of edges or dilution of fine details in an image. Noise may occur due to the following reasons:

·         Physical Nature of the system

·         Due to image Acquisition devices

·         Due to the Environment

·         Image Developing Mechanism

There are basically three types of primary Noise.Random, Fixed Pattern,and Banding. Random type of the Noise can Increase the Intensity of the Picture. When the intensity changes it occurs through color discrepancies above and below. It is random even if same settings are used. In this Noise occurs randomly throughout the image. Random Noise is affected by exposure length. Random Noise is hardest to get rid of because we cannot predict when it occurs. The digital camera cannot account for it and it has to be lessened in an image editing program. 

Fixed Pattern noise surrounds hot pixels. These hot pixels are much more intense than other surroundings, and this type of noise is much better than Random Noise fluctuations. High temperature and long exposure cause the fixed pattern to appear. The hot pixels will occur in same place and time, if pictures are taken under the same settings after the fact fixed pattern type of noise is easiest to fix. It can adjust to lessen the effect on the image if once a digitized camera realizes the fixed pattern. If it is not lessened than it can be more dubious to the eye than the random Noise.

Banding type of noise will depends upon camera as not all digital cameras will create it.the digital camera takes the data being produced from the sensor and creates the noise .during the data processing steps. Shadows, Photo brightening and high speeds will create banding Noise.

1.3.1 Noise Source

There are various sources of noise such as:

·         While capturing an image movement of camera may cause addition of noise in image which also cause blurness and image is distorted.

·         With various sources like increment of temperature (thermal sources) also contribute in addition of noise in the images.

·         Bit errors in image transmission causes addition of Salt and Pepper noise in the image.

·         Scratch in an image is also cause of noise

·         Electronic form of noise is cause of Quantization error.

·         Noise can also be caused due to lens abnormality. 

1.3.2Types of Noise:

·         Impulse Noise

·         Gaussian Noise

·         Additive White Gaussian Noise(AWGN)

·         Shot Noise

·         Quantization Noise

·         Anisotropic Noise

·         Multiplicative Noise

 Impulse Noise: Unwanted, instantaneous sharp clicks in image are categorized as Impulse Noise. Electromagnetic inference or ill synchronization in recording of digital images usually causes noise of this kind. Median filter is used for removal of impulse noise. Impulse noise is also known as salt and pepper noise.

Gaussian Noise:Gaussian noise represents statistical noise having probability density function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution. The Cause of Gaussian noise in digital images is during acquisition such as due to poor illumination sensor noise is caused else due to high temperature electronic circuit noise is caused. For reduction of Gaussian noise various filters are used such as spatial filter, though when smoothing an image, an undesirable outcome may result in the blurring of fine-scaled image edges and details because they also correspond to blocked high frequencies. Conventional spatial filtering techniques for noise removalinclude: mean (convolution) filtering, median filtering and Gaussian smoothing.

Additive White Gaussian Noise (AWGN): AWGN is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics:

·         'Additive' because it is added to any noise that might be intrinsic to the information system.

·         ‘White' refers to idea that it has uniform power across the frequency band for the information system. It is an analogy to the color white which has uniform emissions at all frequencies in the visible spectrum.

·         'Gaussian' because it has a normal distribution in the time domain with an average time domain value of zero.

Shot Noise:Shot noise is a type of electronic noise which originates from the discrete nature of electric charge. This type of noise is added at the time of capturing of an image.

Quantization Noise: The difference between input and output is named the quantization error. Therefore, the quantization error can be between -1/2Q and +1/2Q.This error can be considered a quantization noise with RMS:

Q can be calculated by dividing the range of the ADC by the number of steps in the staircase.

In the above equation, N is the number of bits of the ADC and the input range can be somewhere between 0 and , Where ADC is Analog-Digital-Converter.

Anisotropic Noise:This type of noise is occurred when image is captured at oblique viewing angles with the projected camera. For removal of anisotropic noise filter used is anisotropic filter which reduces and preserves detail at extreme viewing angles.

Multiplicative Noise:It is unwanted random signal that gets multiplied into some relevant signal during capture, transmission, or other processing.  Examples of multiplicative noise affecting digital photographs are proper shadows due to undulations on the surface of the imaged objects, shadows cast by complex objects like foliage and Venetian blinds, dark spots caused by dust in the lens or image sensor, and variations in the gain of individual elements of the image sensor array.

1.4Speckle Noise

Speckle is a granular 'noise' that inherently exists in and degrades the quality of the active radar and synthetic aperture radar (SAR) images.

Speckle noise in conventional radar results from random fluctuations in the return signal from an object that is no bigger than a single image-processing element. It increases the mean grey level of a local area.

Difficulties for image interpretation, Speckle noise in SAR are generally more serious. It is caused by coherent processing of backscattered signals from multiple distributed targets. In SAR oceanography, for example, speckle noise is caused by signals from elementary scatterers, the gravity-capillary ripples, and manifests as a pedestal image, beneath the image of the sea waves.

Based upon different mathematical models of the phenomenon several different methods are used to eliminate speckle noise, One method, for example, employs multiple-look processing (a.k.a. multi-look processing), averaging out the speckle noise by taking several "looks" at a target in a single radar sweep. The average is the incoherent averageof the looks.

A second method involves using adaptive and non-adaptive filters on the signal processing (where adaptive filters adapt their weightings across the image to the speckle level, and non-adaptive filters apply the same weightings uniformly across the entire image). Such filtering also eliminates actual image information as well, in particular high-frequency information, and the applicability of filtering and the choice of filter type involves tradeoffs. Adaptive speckle filtering is better at preserving edges and detail in high-texture areas (such as forests or urban areas). Non-adaptive filtering is simpler to implement, and requires less computational power.

There are two forms of non-adaptive speckle filtering: one based on the mean and one based upon the median (within a given rectangular area of pixels in the image). The latter is better at preserving edges whilst eliminating noise spikes, than the former is. There are many forms of adaptive speckle filtering, including the Lee filter, the Frost filter, and theRefined Gamma Maximum-A-Posteriori (RGMAP) filter. They all rely upon three fundamental assumptions in their mathematical models, however:

·         Speckle noise in SAR is a multiplicative noise, i.e. it is in direct proportion to the local grey level in any area.

·         The signal and the noise are statistically independent of each other.

·         The sample mean and variance of a single pixel are equal to the mean and variance of the local area that is centered on that pixel.

Speckle is a noise variation in contrast. But it is not a noise in an image. It occurs from Random Variations in the backscattered waves from an object and it will mostly see in Ultrasound imaging and synthetic aperture Radar Imaging.Basically there are two mathematically models of Noise. Additive Noise which can be removed or reduced very easily and it is systematic in Nature. Whereas Multiplicative Noise which cannot be removed very easily and hence it is complex to model and difficult to remove. Due to the de phased echoes from the appeared scatters, multiplicative noise is generated is termed as “Speckle Noise”. It seems to be as noise but it contains some useful information because it is due to the surroundings of the target. In different imaging systems Speckle may appear distinct but it is always in granular patter due to the image formation under coherent waves.

When a Sound Waves pulse randomly interferes with the small particle or object that is comparable to sound wavelength, it generates diffuse scattering which is termed as “Speckle Noise”. Ultrasound Images and SAR images is an inherent property of Speckle Noise. In most of the cases, it is considered as a contaminating factor that severely degrades the image quality. To improve image analysis it is generally used for two applications.

·         Auto Segmentation

·         Visual Enhancement

 For enhancing visualization of Speckle Images many filters were developed. Their main applications are in two areas SAR and Ultrasound images.

In Medical imaging Ultrasound is very popular due to its low cost, real time system and small in size and less harmful to human body. But the major disadvantage is the presence of speckle. 

Figure: 1.2(b)Noisy image with 0.5 deviation            Figure: 1.3(c)Noisy image with 0.75 deviation               

Fig: 1.1 Image Corrupted with Speckle Noise With different Standard deviations () of noise (a) Original Synthetic Image without Noise. (b) Synthetic Image having speckle noise whose Standard deviation is 0.5 (c) Synthetic Image having speckle noise whose Standard deviation is 0.75.

1.4.1Disadvantages of Speckle Noise

·         Ultrasound pulses always travel in straight line to and fro from reflecting interference due to incorrect assumption.

·         Another Source of Reverberations is that a small portion of the returning sound  pulse  may be reflected back in to the tissues by  the transducer surface itself and generate the new echo at twice the depth.

1.4.2 Common Speckle Filters

There are two major classifications of speckle reduction filters, viz. single scale spatial filters and transform domain multiscale filters. The spatial filter acts on an image by smoothing it; that is, it reduces the intensity variation between adjacent pixels. The simple sliding window spatial filter replaces the center value in the window with the average of all the neighboring pixel values including it. By doing this, it replaces pixels that are unrepresentative of their surroundings. It is implemented with a convolution mask, which provides a result that is a weighted sum of the values of a pixel and its neighbors. It is also called a linear filter. The mask or kernel is a square. Often a 3× 3 square kernel is used. If the coefficients of the mask sum up to one, then the average brightness of the image is not changed. If the coefficients sum to zero, the average brightness is lost, and it returns a dark image.

1.4.3Lee Filter:

This lee based is based on the approach. It depends upon the variance. If variance over anarea is low or constant then the smoothing will occurs. If the variance is high then the smoothing will not be performed. The lee filter assumes that speckle noise is multiplicative. Than the SAR image can be approximated by a linear model gives the equation

Img (i,j)=+W*(




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