# Combining two images

I am working with speckle noise reduction in ultrasound images. I have used wavelet transform for removing the noise by eliminating certain frequencies in order to eliminate any existing noise. Since in an image HH,LH,HL components contains most of the noise. We can eliminate noise by eliminating those components.

  step 1 : read an input image.
step 2 : apply discrete wavelet transform.
step 3 : Eliminate LH, HL, HH  by making these components zero.
step 4 : Take inverse wavelet transform(let us consider this as output 1).
step 5 : read the same input image and again take discrete wavelet transform.
step 6 : eliminate LL component by making zero and keep LH,HL & HH because it contains edge information. (trying to remove noise from the edge information & add it back to Output 1)
step 7 : take inverse wavelet transform .
step 8 : Applying a Hybrid Filter (Median- Weiner) to the above image
step 9 : We get the filtered image ( let us consider this as output 2)


I have represented the same in the below figure.

Now, I need to combine output 1 and output 2 . I just added both the outputs but am not getting proper output . Please suggest me the technique which I should use to combine these two output images. Kindly tell me whether it is possible or not and also tell me whether this concept is correct or wrong.  ## 2 Answers

You can implement discrete wavelet transforms on output1 and output2. Use LL from output1 and LH, HL, and HH to form a new block, then implement inverse wavelet transform.

• Thank you , Actually i planned of using inverse wavelet transform to combine images at the next stage.please see the updated block diagram.Is there any other way to combine these images without using IDWT. – preethi Feb 16 '14 at 1:49
• I'm not sure if that will give any different results. With two separate images, you get ouputs: $\frac{a\times LL}{(a+b+c+d)}$ and $\frac{(b\times LH+c\times HL+d\times HH)}{(a+b+c+d)}$. Adding them, or combining the four filtered parts and performing the IDWT appears to be the same, unless you want to weight the edge image - which is equivalent to weighing the IDWT coefficients. – tpb261 May 20 '15 at 6:04

It all depends on the part you called ,,fusion''. Just adding the images would result in the original image, because of linearity of DWT. It is not very clear what you are trying to achieve (what is ,,proper'' in your sense). Probably you want to emphasize a drawing.

The following ideas appeared:

1. Noise reduction and edge preservation seem to contradict each other and might be subject to a trade-off.
2. You might want to just weigh the DWT coefficients, instead of first splitting the fields. There appears be no advantage in doing so.
3. One level of a DWT will not give much room to reason about preserving edges.
• When we just add those two outputs, we get a image which has more noise ... Subjective quality is poor.. PSNR and SNR also decrease ..what do you mean by weighing DWT coefficients? Can you elaborate? If we go more level of dwt , it will decrease image quality right ? We will loose more image details – Premnath D Feb 24 '14 at 2:03
• Actually, noise reduction is often just scaling or weighting the DWT coefficients before the inverse transform. Zeroing coefficients (as you do in both ways) is just multiplying then with zero. The more coefficients you delete that way, the less information will be left, obviously. – user7358 Feb 24 '14 at 8:03
• Then how to reduce noise without making them zero.. I mean how to weigh the DWT coefficients? Suggest me with an example – Premnath D Feb 24 '14 at 11:45
• Maybe you set all below a certain threshold to zero. This method is rather popular. You could also use different thresholds in different contexts (levels), or even weigh depending on other coefficients. If you have a sharp border, coefficients of different levels will be correlated. – user7358 Feb 24 '14 at 15:17
• please suggest the best fusion technique that could be used after using thresholding methods to reduce noise. – preethi Feb 24 '14 at 17:04