Wiener discrete cosine transform-based image filtering

Abstract

Abstract. A classical problem of additive white (spatially uncorrelated) Gaussian noise suppression in grayscale images is considered. The main attention is paid to discrete cosine transform (DCT)-based denoising, in particular, to image processing in blocks of a limited size. The efficiency of DCT-based image filtering with hard thresholding is studied for different sizes of overlapped blocks. A multiscale approach that aggregates the outputs of DCT filters having different overlapped block sizes is proposed. Later, a two-stage denoising procedure that presumes the use of the multiscale DCT-based filtering with hard thresholding at the first stage and a multiscale Wiener DCT-based filtering at the second stage is proposed and tested. The efficiency of the proposed multiscale DCT-based filtering is compared to the state-of-the-art block-matching and three-dimensional filter. Next, the potentially reachable multiscale filtering efficiency in terms of output mean square error (MSE) is studied. The obtained results are of the same order as those obtained by Chatterjee's approach based on nonlocal patch processing. It is shown that the ideal Wiener DCTbased filter potential is usually higher when noise variance is high.

Prediction of filtering efficiency for DCT-based image denoising

“…This potential output MSE considerably depends on image complexity and increases proportionally to noise variance, but not linearly (if noise variance increases twice, output MSE becomes larger by about 1.6 times for most images). This means that the most complicated task is to provide high efficiency of noise removal for complex-structure images if noise variance is not large (similar results and conclusions have been obtained in [7] where potential of image denoising is analyzed within Wiener and DCT filtering approach).…”

Is Texture Denoising Efficiency Predictable?

“…The following procedure has been proposed in Ref. 26. The initial step 1 is to skip¯ltering if P 0:5 < 0:25.…”

“…50 Recently, the powerful clustering-based denoising schemes have been proposed: KSVD 43 and KLLD 3 that use learned dictionaries in di®erent ways, and a¯lter based on gradient histogram preservation (GHP). 54 Their analysis has shown that most of the aforementioned denoising techniques perform similarly (approximately at the same level as standard DCT-based¯lter 22,26 and BM3D¯lter 11 ) whilst NLM and LPG-PCĀ lters 4,6 perform su±ciently worse. Moreover, it is worth performing a more careful analysis.…”

“…Therefore, a task is to remove this noise preserving the texture features in a maximally careful manner. 17,32,35,36,46,54 One might expect that this task of e±cient texture denoising which was already relevant a decade or two ago, 17,32,46 and now with all recent advancements (nonlocal ltering methods) in image denoising 11,12,14,26,46 has been successfully solved. However, this is not true.…”

“…27 It has been shown in Refs. 35 and 36 that the problems in noise removal arise for¯lters based on discrete cosine transform (DCT) 16,22,26 and one of the most advanced nonlocal¯l-tering methods, BM3D (block matching three dimensional)¯lter. 11 Then, one might think that denoising techniques based on other principles are able to cope with a noise in texture images in a better way.…”