Can you provide references of works that analyze the computational complexity of the wavelet transform for image analysis.
Hello Vyacheslav! Please, take a look at these papers and scientific works:
1) http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1217267&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1217267
2) http://www.sciencedirect.com/science/article/pii/S1077316985710222
3) http://www.sensorsportal.com/HTML/DIGEST/September_2013/P_1369.pdf
4) "Calibração Multivariada Empregando Transformada Wavelet Adaptativa" (It is written in brazilian portuguese. However, you can translate it to english using some tool like google translator)
5) "Identificação de Imagem com Análise em Multiresolução Wavelet em Sistema"
Best regards and good luck with your research!
In wavelet transform implementation,there are 2 filters namely low pass filter and High pass filter.When you decompose an image there are 2 sets of processing involved one is row processing and another is column processing.First every row has to be convoluted with low pass filter coefficients and down sampled by 2 and the same row has to be convoluted with high pass filter coefficients and down sampled by 2.
The same process has to be repeated for every row and has to be repeated for every column after row processing.After the overall computation you will get 4 bands namely 'LL','LH','HL','HH'. It is well known that convolution involves multiplication and addition. This is termed to be computational complexity.
If there is Discrete wavelet transform (DWT) followed by Inverse discrete wavelet transform (IDWT) there is no loss in the information.you will get exact quality of the image after reconstruction.The computational complexity is as mentioned in the above answer.When you introduce quantization after wavelet decomposition there is a loss in the quality of the image which is normally measured by a parameter called Peak signal to noise ratio(PSNR in dB).The computational complexity is more if quantization is also involved
The Wavelet Transform may be written as a convolution product, thus as such, you may resort to the convolution theorem and compute the Wavelet Transform in the frequency domain. By doing so, the Wavelet Transform is reduced to a pointwise multiplication between the FFT of your input image and the FFT of your dilated, rotated and translated wavelet. Hence, the overall computational complexity would be dominated by the FFT transform costs for the inputs, which is O(NlogN), N being each input size.
J. Opt. Soc. Am. A/Vol. 24, No. 5/May 2007 - "Automated segmentation of retinal blood vessels and identification of proliferative diabetic retinopathy"
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