3D DCT Based Filtering of Color and Multichannel Images

Efficiency analysis of color image filtering

“…However, there are initial results showing that MSE lb values in this case should be considerably smaller than in the case of component-wise processing [51,53]. We present results (output MSE 3DDCT ) for the 3D DCT based vector filter [33] that uses "spectral" DCT to decorrelate color components and then applies 2D DCT (see data in Table 2 for noise variances σ 2 = 65 and σ 2 = 130). Let us, for example, consider MSE 3DDCT for the test image #13.…”

“…As examples, let us give data for two images from TID2008: one of the simplest ones (#3) and one of the most complex (#13). If the 3D DCT filter [33] [33,53] are able to provide even larger increase of PSNR after denoising.…”

“…The sixth reason is that images to be filtered can be onechannel (grayscale) [10,13], three-channel (as color images in RGB representation) [1,2,6], and multichannel (e.g., multi-and hyperspectral) [3,4]. For filtering multichannel images, two approaches are possible, namely, component-wise denoising and vector or 3D processing taking into account inter-channel correlation of image data [1,2,6,12,33,34]. Each of them has advantages and shortcomings.…”

“…One problem is that in most books and papers that address color image filtering, noise is supposed to be independent and identically distributed (i.i.d.) [6,12,33]. This is an idealization that leads to overestimation of (expected) filtering efficiency that is reachable in practice [35][36][37].…”

“…A lot of vector filters that allow exploiting inherent inter-channel correlation of color image components have been proposed since then [6,12]. In this article, we basically consider DCT-based filters [15,33,35,47] since they have shown themselves to be quite simple, efficient, and easily adaptable to processing grayscale and color images corrupted by i.i.d. and spatially correlated noise.…”