cite{1} The median filter is one of usual filters used to reduce noise in holography images. The median filter considers each pixel and its nearby neighbor’s values and replaces it with the median of these values. In statistics, median is calculated by sorting all values and selecting the value in the middle of sorted values. If the neighborhood (window size) under consideration contains an even number of pixels, the average of two middle pixel values is used as median. Specially in some noises such as salt and pepper, the median filter is the best filter.


subsubsection {Bm3d}

cite{2}In some holography denoising recent methods, the pixels of image is classified into heterogeneous regions and then different methods and parameters are used to denoising these regions. In the pixels belonging to each region, the noise distribution is supposed similar and the type and parameters of denoising method keep constant. This type of filtering, that in fact, is a dynamic and semantic denoising process is known as block matching. The main challenge with this type of filtering is finding heterogeneous regions. Many unknown steps are affect this process, for example search window size, the metric for measuring similarity in blocks, the similarity threshold, etc… Once the similar blocks are obtained, blocks belonging to similar regions are clustered, the noise parameters of these regions estimated locally and each region filtered through local filtering.

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subsubsection {Winer}

cite{3} In simple and 2d signal (image) processing, the inverse filtering is a restoration technique for deconvolution. In holography image, when the image is blurred by a semi-known noise in the low-frequency band, it is possible to recover the image by inverse filtering. This reverse filtering is very susceptible to augmentative noise. The Wiener filtering obviates this issue. This filter performs an optimal exchange between inverse filtering and noise smoothing. It obliterates the additive noise and inverts the blurring altogether (That is so critical in holography images). Actually, this filtering is optimal in terms of the mean square error. It minimizes the total mean square error in the process of noise smoothing. The Wiener filtering is a linear conjecture of the original image. The main debility of Wiener process is its Gaussian-based denoising step.


subsubsection {NLM}

cite{4}Non-local means filtering takes a mean of all pixels in the image, weighted by how similar these pixels are to the target pixel. This results in much greater post-filtering clarity, and less loss of detail in the image compared with local mean algorithms. Recently non-local means has been combine to block matching (BM) method to improve denoising performance. Unlike the local mean or median filters, which take the mean or median value of a group of pixels belonging to a window or block, non-local means filtering takes a mean of all pixels in the heterogeneous regions or in all image pixels weighted by how similar these pixels are to the target pixel. Similar to block matching algorithm, the main challenge with this type of filtering is finding heterogeneous regions. Many unknown steps are affect this process, for example search window size, the metric for measuring similarity, etc… Once the similarity metric defined, the weight for pixels is determined and weighted mean filtering method is applied to each pixel.


subsubsection {Spadadh}

cite{5} Nonlocally centralized sparse representation is an effective approach for estimating original image from a noisy image. In the first step of this method, sparse coefficients from all regions (including regions segmented) is extracted.  The main challenge of this method is to extract sparse coefficients more accurate. After this step the image is classified into different types according to the statistical characteristics of sparse coefficients. For each type of regions, similar to block matching or NLM, an appropriate denoising method is selected. window size or segmentation method, the form of sparse coefficients, similarity or distance measure that used for finding clusters are some of other challenges in this type of denoising.


subsubsection {Lee}

Synthetic Aperture Radar filtering is so similar to holography images. If the noise model is supposed multiplicative in SAR or holography images, many of denoising methods is inefficient.  Lee proposed an adaptive filter cite{6} for solving this problem. The Lee filter can be described by egin{equation}


d(x,y) = alpha s(x,y) + (1 – alpha {mu _s})                                 (1)

In Lee filter, Parameter a = 1 – C_b^2/C_s^2 depends on the ratio of the squares of the local variation coefficients of the image, Cs, and noise, Cb. This local variation coefficient is defined as the ratio of the variance between the mean square of the considered pixel values. In a region with homogeneous(constant) values, the local variation coefficient is low and the filter does not modify pixel value and vice versa. Lee filter uses the minimum mean square error filtering criterion to carry out the despeckling (such as wiener filter that is optimal in gaussian process)

subsubsection {Frost}

In cite{7} Frost modified Lee filter. For holography and SAR images, frost showed that the dominant noise is a multiplicative noise. Frost model, leads to the functional form of an adaptive, minimum MSE filter for smoothing SAR and holography images. . As a modification of Lee method, this filter uses NLM and BM methods in combination to Lee method for better denoising. By using block matching and estimate noise parameters inside homogeneous areas of an image this filter preserves the edge structure. It is shown in cite{7} that this filter can be easily implemented in the spatial domain and is computationally efficient


subsubsection {Wavelet}

Wavelet denoising is a very powerful non-linear technique, which operates in time-frequency domain. In its most basic form, each coefficient is compared with threshold, if the coefficient is smaller than threshold, set to zero; otherwise it is kept or modified. The main parameters of this method is its wavelet function, decomposition levels and the form of finding threshold. If the original image corrupted by Gaussian noise, threshold is found by a Bayesian technique using probabilistic model of the image wavelet coefficients that are dependent on generalized Gaussian distribution. In the simple wavelet denoising method the noise considers an additive noise. When the noise is multiplicative, additive signal and noise are obtained by computing the logarithm. This was studied in the case of speckle noise processing in SAR imagescite{8}.


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