Overview
The Speckle function removes speckle in radar datasets and smooths out noise, while retaining edges and sharp features in the image. Speckle is the highfrequency noise that exists in radar images. The images generated by laser, ultrasound, and synthetic aperture radar (SAR) systems are subject to speckle noise due to the interference of the returning electromagnetic waves scattered from multiple surfaces. The Speckle function uses mathematical models to filter the bright and dark spots that are generated as a result of interference, to allow better image interpretation.
Notes
Smoothing algorithms in the Speckle function reduce and filter speckle using the Lee, Enhanced Lee, Frost, or Kuan filter types.
For optimal speckle reduction, you can try the following:
 Filter Size greatly affects the quality of processed images. A 7by7 filter usually gives good results with moderate smoothing.
 Number of Looks is used to estimate noise variance, and it effectively controls the amount of smoothing applied to the image by the filter. A smaller value leads to more smoothing; a larger value preserves more distinct image features.
 Apply a histogram stretch to adjust the contrast or brightness of the image.
Lee filter
The Lee filter reduces the speckle noise by applying a spatial filter to each pixel in an image, which filters the data based on local statistics calculated within a square window. The value of the center pixel is replaced by a value calculated using the neighboring pixels. With the Lee filter, you can choose to reduce additive noise, multiplicative noise, or both. Use the Lee filter to smooth speckled data that has an additive or multiplicative component.
Noise model  Algorithm  Variable definitions 

Additive 
where
 P_{C}—Center pixel value of window L_{M}—Local mean of filter window L_{V}—Local variance of filter window M—Multiplicative Noise Mean A—Additive Noise Mean AV—Additive noise variance MV—Multiplicative noise variance SD—Standard deviation of filter window NLooks—Number of Looks 
Multiplicative 
where
 
Additive and multiplicative  where

Note:
The Additive Noise Mean value is usually 0. The Multiplicative Noise Mean value is usually 1.
Enhanced Lee filter
The Enhanced Lee filter is a refined version of the Lee filter, reducing the speckle noise effectively by preserving image sharpness and detail. It requires a Damping Factor and Number of Looks. Use the Enhanced Lee filter to reduce speckle while preserving texture information.
Algorithm  Variable definitions 

Value of smoothed center pixel =
where
 P_{C}—Center pixel value of window L_{M}—Local mean of filter window SD—Standard deviation in filter window NLooks—Number of Looks D—Damping Factor 
Frost filter
The Frost filter reduces speckle noise and preserves important image features at the edges with an exponentially damped circularly symmetric filter that uses local statistics within individual filter windows. The Frost filter requires a Damping Factor. Use the Frost filter to reduce speckle while preserving edges in radar images.
Scene reflectivity is an important factor that differentiates the Frost filter from the Lee and Kuan filters. It is calculated by combining the observed image with the impulse response of the SAR system.
Algorithm  Variable definitions 

The implementation of this filter consists of defining a circularly symmetric filter with a set of weighting values M for each pixel.
The resulting graylevel value of the filtered pixel is
where
 S—Absolute value of the pixel distance from the center pixel to its neighbors in the filter window D—Damping Factor L_{M}—Local mean of filter window L_{V}—Local variance of filter window P1,P2,...Pn—Gray levels of each pixel in the filter window K1,K2,...Kn—Weights (as defined above) for each pixel 
Kuan filter
The Kuan filter follows a similar filtering process to the Lee filter in reducing speckle noise. This filter also applies a spatial filter to each pixel in an image, filtering the data based on local statistics of the centered pixel value that is calculated using the neighboring pixels. The Kuan filter requires the Number of Looks, which controls image smoothing and estimates noise variance. Use the Kuan filter to reduce speckle while preserving edges in radar images.
Algorithm  Variable definitions 

Filtered pixel value is
where

P_{C}—Center pixel value of window L_{M}—Local mean of filter window L_{V}—Local variance of filter window NLooks—Number of Looks 
Parameters
Parameter  Description 

Raster  The input raster. 
Filter Type  Specifies the filter type to be used in the smoothing algorithm to remove speckle noise:

Filter Size  Specifies the size of the pixel window used to filter noise:

Noise Model  Specifies the type of noise that is reducing the quality of the radar image:

Noise Variance  Specifies the noise variance of the radar image. This parameter is only valid when the Filter Type is Lee Filter and the Noise Model is Additive Noise or Additive and Multiplicative Noise. The default value is 0.25. 
Additive Noise Mean  Specifies the mean value of additive noise. A larger noise mean value will produce less smoothing, while a smaller value results in more smoothing. This parameter is only valid when the Filter Type is Lee Filter and the Noise Model is Additive Noise or Additive and Multiplicative Noise. The default value is 0. 
Multiplicative Noise Mean  Specifies the mean value of multiplicative noise. A larger noise mean value will produce less smoothing, while a smaller value results in more smoothing. This parameter is only valid when the Filter Type is Lee Filter and the Noise Model is Additive Noise or Additive and Multiplicative Noise. The default value is 1. 
Number of Looks  Specifies the number of looks of the image, which controls image smoothing and estimates noise variance. A smaller value results in more smoothing, while a larger value retains more image features. This parameter is only valid when the Filter Type is Lee Filter and the Noise Model is Multiplicative Noise, or when the Filter Type is Kuan Filter. The default value is 1. 
Damping Factor  Specifies the extent of exponential damping effect on filtering. A larger damping value preserves edges better but smooths less, while a smaller value produces more smoothing. A value of 0 results in the same output as a lowpass filter. This parameter is only valid when the Filter Type is Enhanced Lee Filter or Frost Filter. The default value is 1. 