The vast majority of surfaces, synthetic or natural, are extremely rough on the scale of the wavelength. Images obtained from these surfaces by coherent imaging systems such as laser, SAR, and ultrasound suffer from a common interference phenomenon called speckle. The origin of this phenomenon is seen if we model our reflectivity function as an array of scatterers. Because of the finite resolution, at any time we are receiving from a distribution of scatterers within the resolution cell. These scattered signals add coherently; that is, they add constructively and destructively depending on the relative phases of each scattered waveform. Speckle results from these patterns of constructive and destructive interference shown as bright and dark dots in the image 
Although commonly referred to as "speckle noise", speckle is not noise in its generally understood sense of an unwanted modification to a desired signal. Rather, it is the signal itself that fluctuates, because the scatterers are not identical for each cell, and the signal is highly sensitive to small variations in scatterers.
Speckle in conventional radar increases the mean grey level of a local area.
Speckle in SAR is generally serious, causing difficulties for image interpretation. It is caused by coherent processing of backscattered signals from multiple distributed targets. In SAR oceanography, for example, speckle is caused by signals from elementary scatterers, the gravity-capillary ripples, and manifests as a pedestal image, beneath the image of the sea waves.
The speckle can also represent some useful information, particularly when it is linked to the laser speckle and to the dynamic speckle phenomenon, where the changes of the speckle pattern, in time, can be a measurement of the surface's activity.
Several different methods are used to eliminate speckle, based upon different mathematical models of the phenomenon. One method, for example, employs multiple-look processing (a.k.a. multi-look processing), averaging out the speckle by taking several "looks" at a target in a single radar sweep. The average is the incoherent average of 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, however.
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 spikes, than the former is. There are many forms of adaptive speckle filtering, including the Lee filter, the Frost filter, and the Refined Gamma Maximum-A-Posteriori (RGMAP) filter. They all rely upon three fundamental assumptions in their mathematical models, however:
- Speckle in SAR is a multiplicative, i.e. it is in direct proportion to the local grey level in any area.
- The signal and the speckle 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 centred on that pixel.
The Lee filter converts the multiplicative model into an additive one, thereby reducing the problem of dealing with speckle to a known tractable case.
Recently, the use of wavelet transform has led to significant advances in image analysis. The main reason for the use of multiscale processing is the fact that many natural signals, when decomposed into wavelet bases are significantly simplified and can be modeled by known distributions. Besides, wavelet decomposition is able to separate signals at different scales and orientations. Therefore, the original signal at any scale and direction can be recovered and useful details are not lost.
The first multiscale speckle reduction methods were based on the thresholding of detail subband coefficients. Wavelet thresholding methods have some drawbacks: (i) the choice of threshold is made in an ad hoc manner, supposing that wanted and unwanted components of the signal obey their known distributions, irrespective of their scale and orientations; and (ii) the thresholding procedure generally results in some artifacts in the denoised image. To address these disadvantages, non-linear estimators, based on Bayes' theory were developed.
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