Total views : 314

Least Square based Image Denoising using Wavelet Filters


  • Centre for Computational Engineering and Networking (CEN), Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Amrita University, Coimbatore, Tamil Nadu - 641112, India


Background/Objectives: Noise in a digital image, is unwanted information that degrades the quality of an image. The main aim of the proposed method is to denoise a noisy image based on least square approach using wavelet filters. Methods/ Statistical Analysis: One dimensional least square approach proposed by Selesnick is extended to two dimensional image denoising. In our proposed technique of least square problem formulation for image denoising, the matrix constructed using second order filter coefficients is replaced by wavelet filter coefficients. Findings: The method is experimented on standard digital images namely Lena, Cameraman, Barbara, Peppers and House. The images are subjected to different noise types such as Gaussian, Salt and Pepper and Speckle with varying noise level ranging from 0.01db to 0.5db. The wavelet filters used in the proposed approach of denoising are Haar, Daubechies, Symlet, Coiflet, Biorthogonal and Reverse biorthogonal. The outcome of the experiment is evaluated in terms of Peak Signal to Noise Ratio (PSNR). The analysis of the experiment results reveals that performance of the proposed method of least square based image denoising by wavelet filters are comparable to denoising using existing second order sparse matrix. Applications/Improvements: Digital images are often prone to noise; hence, proceeding with further processing of such an image requires denoising. This work can be extended in future to m-band wavelet filters.


Image Denoising, Least Square, Peak Signal to Noise Ratio (PSNR), Wavelet Filters.

Full Text:

 |  (PDF views: 264)


  • Singh I, Chand L. Image denoising techniques: A review. International Journal of Engineering Research and Technology. 2013 Apr; 2(4):1-4.
  • Anutam R. Image denoising techniques: An overview. International Journal of Computer Applications. 2014 Jan; 86(16):1-5.
  • Kehua Su, Hongbo Fu, Bo Du, Hong Cheng, Haofeng Wang, Dengyi Zhang. Image denoising based on learning overcomplete dictionary. International Conference on Fuzzy Systems and Knowledge Discovery; 2012 May; p. 395–8 .
  • Rajwade J, Rangarajan A, Banerjee A. Image denoising using the higher order singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2013 Apr; 35(4):849–62.
  • Khare AS, Mohan R, Sharma S. An efficient image denoising method based on fourth-order partial differential equations. IJACR. 2013 Mar; 3(1):1-6.
  • Sowmya V, Neethu Mohan, Soman KP. Sparse banded matrix filter for image denoising. Indian Journal of Science and Technology. 2015 Sep; 8(24):1-6.
  • Lebrun M, Buades A, Morel JM. A nonlocal Bayesian image denoising algorithm. SIAM Journal on Imaging Sciences. 2013 Jun; 6(3):1665–88.
  • Deepa M, Saravanan T. Automatic image registration using 2D discrete wavelet transforms. Indian Journal of Science and Technology. 2016 Feb; 9(5):1-3.
  • Vijay M, Saranya Devi L, Shankaravadivu M, Santhanamari M. Image denoising based on adaptive spatial and wavelet thresholding methods. International Conference on Advances in Engineering, Science and Management (ICAESM); 2012 Mar. p. 161–6.
  • Yan R, Shao L, Liu Y. Nonlocal hierarchical dictionary learning using wavelets for image denoising. IEEE Transactions on Image Processing. 2013 Dec; 22(12):4689-98.
  • Aarthy G, Amitha P, Krishnan T, Pillai GS, Sowmya V, Soman KP. A comparative study of spike and smooth separation from a signal using different over complete dictionary. International Multi-Conference on Automation, Computing, Communication, Control and Compressed Sensing (iMac4s); 2013 Mar. p. 590–5.
  • Selesnick I. Least Squares with Examples in Signal Processing. 2013 Mar.
  • Soman KP, Resmi NG, Ramachandran KI. Insight into Wavelets: From Theory to Practice. 3rd ed. PHI Learning Pvt. Ltd.; 2010.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.