Multilook Technique for speckle reduction

Consider a stack of images  affected by speckle noise of a same scene. 

In order to reduce the speckle, the availability of the stack of images can be utilized to obtain speckle reduced image.

In order to understand the multilook technique, let’s first generate noisy images and then apply speckle reduction.

Generate stack of noisy images:

1.      Read a noise free image

2.      Generate exponential noise with mean 1 and multiply it with the noise free image

3.      Repeat the process of generating exponential noise and multiplying  it with the noise free image to create stack of ‘n’ images

MATLAB code:

%Multilook - Speckle reduction

%Read a noisy free Image

I = imread('cameraman.tif');

I = double(I);

figure,imagesc(I);colormap(gray);title('Original Image');

[m, n] = size(I);

numofimg = 9;

Stack = zeros([m n numofimg]);

for i = 1:numofimg

    %Generate exponential noise

    noise=random('exp',1,m,n);

   

    %Multiply Noise free Image with noise

    Stack(:,:,i)=I.*noise;

   

end

Explanation:

Random noise with exponential distribution is multiplied with the noise free image to generate image affected by speckle.

Fig: Probability Density Function (PDF) of the noise generated for ‘n’ images that follows exponential distribution.

Multilook(ML) Technique:

Multilook image is the average of the stack of images. This technique is used widely in the field of Synthetic Aperture Radar(SAR) to reduce speckle on the same scene but different acquisition periods.

The stack of data is created for the same scene but with different time of acquisition and ML is applied to reduce the speckle considerably since the noise on the single image will be quite high.

MATLAB code:

ML_image = mean(Stack,3);

figure,imagesc(Stack(:,:,1));colormap(gray);title('Single Noisy Image');

figure,imagesc(ML_image);colormap(gray);title('Multilook Image');

Explanation:

For instance, in the above shown image, consider the red dot as the pixel value of the first pixel position of each image in the stack. Add all the pixel values represented in red dot and divide by the number of images in the stack. Similarly, perform the average for the second pixel position (green dot) and so on and so forth for the whole image.

Matlab code ‘mean(Stack,3) ‘ finds the mean of the image in 3^rd dimension and the final result is the Multilooked Image with reduced speckle.

Moving Average Filter:

In order to reduce speckle further, a moving average filter can be used.

Moving average filter of window size 3x3 and 5x5 is applied on the multilook image and window of size 3x3 on a single speckled image in order to appreciate the multilook technique performance.

MATLAB code:

box = ones(3)/9;

ML_avg3 = conv2(ML_image,box,'same');

figure,imagesc(ML_avg3);colormap(gray);title('Moving Average - Window 3 x 3');

box = ones(5)/25;

ML_avg5 = conv2(ML_image,box,'same');

figure,imagesc(ML_avg5);colormap(gray);title('Moving Average - Window 5 x 5');

box = ones(3)/9;

avg_flt = conv2(Stack(:,:,1),box,'same');

figure,imagesc(avg_flt);colormap(gray);title('Moving Average - Single Image');

How to read image file or a complex image file in MATLAB

       Read images that have different file extensions and formats:

• Reading a grayscale or intensity format image
• Reading a RGB or color image
• Reading a complex Image
• Image Format and Machine Format is important

Reading an intensity format Image:

Let’s consider the image extension to be .bin or.img or .dat etc which we can’t read using the MATLAB function imread. Let’s try to read the file and save it in a matrix and use the image for further processing.

Here’s the short procedure:

1. Open the file in read mode

2. Read the data into a matrix

3. Close the file

4. Display the image

MATLAB code:

%Read intensity format Image

fp = fopen('Vesuvius.dat','r');

Imgsize = [746 3680];

Img = fread(fp,Imgsize,'float32');

fclose(fp);

figure,imagesc(Img);

Download link: Vesuvius.dat

EXPLANATION:

In the above example, in order to read and view the image successfully we need two parameters. They are image size and data type.

Normally, for these types of image files there will be a header or information file which contains details about the image or there will be a metadata inside the image file.

For instance, the header file for the above example may look like:

<image xsize="3680" ysize="746"> <info datatype="float32"> <description>Vesuvius.hdr</description> <filename>Vesuvius.dat</filename> </info> </image>

From this file, we can understand the size of the image will be 3680 x 746 and the data type is ‘float32’

Reading a color image:

The RGB image that I use here is of size 497 x 248 and the format is ‘uint8’.

MATLAB code:

fp=fopen('color_image.img','r');

data=fread(fp,[248 497*3]);

fclose(fp);

RGB=zeros([248 497 3]);

Pt=497;

RGB(:,:,1)=data(:,1:Pt);

RGB(:,:,2)=data(:,Pt+1:2*Pt);

RGB(:,:,3)=data(:,2*Pt+1:end);

RGB=uint8(RGB);

figure,imshow(RGB);

Download link: color_image.img

EXPLANATION:

The file content is read into a matrix of size [248 497*3]. The matrix ‘data’ contains Red component, Green component and the blue component. The file format used here is ‘uint8’.

Now let’s see how the data is stored in the file and how it will be retrieved to view in MATLAB.

Consider an RGB matrix of size 5x5. This means that the total pixels in the file will be 5x5x3.So we need to read the 5x5 pixels of Red component, 5x5 pixels of Green component and 5x5 Blue component. All the components are stored in a single matrix and then it is separated as R,G and B components.

In the above image, I1 represents the Red, Green and Blue components separately. And ‘data’ is the contents stored inside the file. All the 3 components are stored adjacent to each other in the file.

Reading Complex Image:

In a complex image, the real and imaginary part of the pixel will be stored adjacent to each other.

All the coherent systems generate complex data such as Synthetic Aperture Radar images, Ultrasound images etc.

MATLAB code:

%Read complex data

fp=fopen('vesuvius_cmplx.img','r');

full_data=fread(fp,[746*2 3680],'double');

fclose(fp);

Real_data=full_data(1:2:end,:);

Imag_data=full_data(2:2:end,:);

complex_data=complex(Real_data,Imag_data);

figure,imagesc(abs(complex_data));colormap(gray);

Download Link: Vesuvius_cmplx.img

NOTE:

The above example image (View of Mount Vesuvius) is an incoherent image which is captured from the illumination of sun. This image does not contain imaginary part or phase. So I manually added a constant phase just for the purpose of making it complex image.

EXPLANATION:

In general, the first row will be real part and the next row will be imaginary part in the complex data file i.e. Real and Imaginary parts will be alternating in each row. This format may differ based on the method of storing the file.

The matrix full_data contains the real and imaginary parts in alternate rows. The ‘complex_data’ which is the final matrix contains the complex data.

Image Format is important!

The data type of the content stored in the file is important as it may misinterpret the data if not mentioned correctly.

For instance, Intensity format SAR images are usually in the double format ie the maximum pixel value can exceed 255.

Consider a matrix A of type ‘double’ if the matrix is converted into unsigned integer of 8 bit format then the value greater than 255 will be rounded up to 255.

After the Matrix A of data type ‘double’ converted to Matrix B of ‘uint8’, the values such as 300,150000 and 89999 are converted to the highest range limit of uint8 ie 255. And the decimal point, 4.44 is rounded up to 4.

Machine Format also need to be considered!

Based on the platform the machine format changes.

Big Endian format:

MATLAB code:

fp = fopen('Vesuvius.dat','r','b');

Imgsize = [746 3680];

Img = fread(fp,Imgsize,'float32');

fclose(fp);

figure,imagesc(Img);

Little Endian format:

fp = fopen('Vesuvius.dat','r','l');

Imgsize = [746 3680];

Img = fread(fp,Imgsize,'float32');

fclose(fp);

figure,imagesc(Img);

EXPLANATION

If the machine format is mentioned explicitly then the file is read in the mentioned order. For instance, consider a file stored in 'Little endian format' but if it is opened in 'Big endian format' then file will be not be read correct. It is also based on the format the local machine supports.

Example for an Image opened with different machine format: 

Lee filter

Let’s realize a Lee filter using MATLAB and C for despeckling of an image. For Lee filter using MATLAB explicitly check : https://www.imageeprocessing.com/2020/07/lee-filter-using-matlab_16.html

Since it’s a patch based processing, the computation cost will be high.

In order to reduce the same, a part of the code is realized in C language for improved performance.

MATLAB code:

%Read an Image

I = imread('coins.png');

%Add multiplicative noise to the image

J = imnoise(I,'speckle',0.01);

figure,imshow(J);

%Apply Lee filter

K = Lee_filter_C(I,J,[5 5]);

figure,imshow(uint8(K));

Create MATLAB function Lee_filter_C :

This function takes the reference image, speckled/noisy image and the window size as input and performs the following steps.

1.     The variance of the reference image is found. Variance can be found either by using MATLAB built-in function or user defined function. Here in this case, a user defined function is used to find the variance.

2.     Based on the size of the kernel, the noisy image is padded with zeros on all sides.

3.     The center index of the kernel is found

4.     The noisy image is processed patch by patch.

5.     The code written in C computelee.c to despeckle the image is used.

MATLAB code:

function Y = Lee_filter_C(R,E,sz)

%R is the Reference Image

%E is the Error or Noisy Image

%K is the Kernel or Window

%Y is the Output Image

% Y = mean(K)+W*(C-mean(K);

% W = variance(K)/(variance(K)+variance(R))

%Define the type

R = double(R);

E = double(E);

%Preallocate the Output Matrix

Y = zeros(size(R));

mn = round((sz-1)/2);

Tot = sz(1,1)*sz(1,2);

EImg = padarray(E,mn);

%Variance of the reference Image

Rvar = myvar(R);

%Rvar = var(R(:));

Indx = floor(median(1:Tot));

for i = 1:size(R,1)

    for j = 1:size(R,2)

        K = EImg(i:i+sz(1,1)-1,j:j+sz(1,2)-1);

        Y(i,j) = computelee(Rvar,K(Indx),K(:)');

       

    end

end

end

NOTE: save the above function as Lee_filter_C.m 

Function to find the variance:

MATLAB code:

function var_v = myvar(I)

I = I(:);

var_v = sum((I-mean(I)).^2)/numel(I);

end

NOTE: Save the above function as myvar.m

C program: computelee.c

Basics on MEX files in MATLAB:

If you are familiar with C programming then we just need to understand the gateway from MATLAB to C programming. The rest of the procedures will be same as we code in c.

The main gateway function for writing the C program is Mex function and it normally takes 4 parameters.

Nlhs – To find number of left hand side parameters

Plhs – Contains all the output parameters in an array

Nrhs – To find the number of right hand side parameters

Prhs – Contains the input parameters in an array

C code:

#include "mex.h"

/* Find variance and mean of the pixels in the window */

void arrayProduct(double v, double In, double *y, double *z, mwSize n)

{

    double VarW,MeanW,W;

    mwSize i;

   

    MeanW=0;

    for (i=0; i

        MeanW=MeanW+y[i];

    }

    MeanW=MeanW/n;

    VarW=0;

    for(i=0;i

    {

        VarW=VarW+((y[i]-MeanW)*(y[i]-MeanW));

    }

    VarW=VarW/n;

   

    W=VarW/(VarW+v);

    z[0]=MeanW+W*(In-MeanW);

}

void mexFunction( int nlhs, mxArray *plhs[],

                  int nrhs, const mxArray *prhs[])

{

    double Rvariance,CIndx,*inMatrix,*out;              

    size_t ncols;               

   

   

    Rvariance = mxGetScalar(prhs[0]);

    CIndx  = mxGetScalar(prhs[1]);

    inMatrix = mxGetPr(prhs[2]);

    ncols = mxGetN(prhs[2]);

   

    plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL) 

    out = mxGetPr(plhs[0]);

    /* Call the function arrayProduct */

    arrayProduct(Rvariance,CIndx,inMatrix,out,(mwSize)ncols);

}

Let’s compare the calling function in MATLAB and the C code for better understanding.

MATLAB code:

computelee(Rvar,K(Indx),K(:)');

Three parameters are passed to the function computeelee.c

1. Variance of the reference image

2. Centre pixel from the kernel

3. All the pixels from the kernel based on the window size

C code:

Rvariance = mxGetScalar(prhs[0]);

CIndx  = mxGetScalar(prhs[1]);

inMatrix = mxGetPr(prhs[2]);

Rvariance contains the variance of the reference image

CIndx contains the centre pixel of the corresponding kernel/patch

inMatrix contains all the pixels of the corresponding kernel/patch

ncols = mxGetN(prhs[2]);

ncols will obtain total number of elements in kernel.

plhs[0] = mxCreateDoubleMatrix(1, 1, mxREAL); 

out = mxGetPr(plhs[0]);

The final result will be stored in the variable ‘outMatrix’.

The function ‘arrayProduct’ written in C language is called to perform the computation.

Steps to be performed:

Let’s see how Lee filter works on homogeneous area and edge based area.

Homogeneous Patch

Edges and lines

The result shows that the filter works well on homogeneous area rather than on edges and lines.

Points to remember when using Mex file:

1.     If you are using the C code for the first time, its better to find the appropriate compiler and configure to use it.

2.     Compile the C code if the compiler is already present and make sure the compilation is successful.

3.     Syntax to setup the compiler: mex  - setup
The above syntax will identify the available compilers in your local system and you can configure it manually.

4.     For compiling the above c code:  mex computelee.c

For successful compilation, the sample output will look like below:

Building with 'lcc-win32'.

MEX completed successfully.

5.     The result of successful compilation will generate computelee.mexw32 for 32 bit system and for 64 bit system, you can find computelee.mexw64 file in your local directory.

To sum up, the two functions Lee_filter_C.m and myvar.m should be placed in the same directory. Computelee.c should also be placed in the same directory and the successful compilation of the same is mandatory.

I hope the readers of my blog will be familiar with working on Mex files. If you need any tutorial or post on this topic, kindly post or mail your suggestions.