The current state-of-the-art non-local algorithms for image denoising have the tendency to remove many low contrast details. Frequency-based algorithms keep these details, but on the other hand many artifacts are introduced. Recently, the Dual Domain Image Denoising (DDID) method has been proposed to address this issue. While beating the state-of-the-art, this algorithm still causes strong frequency domain artifacts. This paper reviews DDID under a different light, allowing to understand their origin. The analysis leads to the development of NLDD, a new denoising algorithm that outperforms DDID, BM3D and other state-of-the-art algorithms. NLDD is also three times faster than DDID and easily parallelizable.

DCT denoising is a classic low complexity method built in the JPEG compression norm. Once made translation invariant, this algorithm was still proven to be competitive at the beginning of this century. Since then, it has been outperformed by patch based methods, which are far more complex. This paper proposes a two-step multi-scale version of the algorithm that boosts its performance and reduces its artifacts. The multi-scale strategy decomposes the image in a dyadic DCT pyramid, which keeps noise white at all scales. The single scale denoising is then applied to all scales, thus giving multiple denoised versions of the low frequency coefficients of the denoised image. A "multi-scale fusion" of these multiple estimates avoids the ringing artifacts resulting from the pyramid recomposition. The final algorithm attains a good PNSR and much improved visual image quality. It is shown to have a deficit of only 1dB with respect to state of the art algorithms, but its complexity is two orders of magnitude lower. Source CodeThe C++ source code, the code documentation, and the online demo are accessible at the IPOL web page of this article web site 1 Compilation and usage instruction are included in the README.txt file of the archive.

In this paper we reconsider the class of patch based denoising algorithms and observe that they under-perform at lower image frequencies. We solve this problem by operating them in a multi-scale structure. Our main observation is that denoising algorithms cannot be trusted with the restoration of high frequency details in the image. Indeed, since denoising algorithms must impose their image prior, the fine details are either smoothed or sharpened in the result. In any case the high frequency properties of the images are altered. This realization has a profound implication on the multi-scale approaches which assume that coarse scale restorations are better denoised and hence are replaced in the finer resolutions. This leads to frequency cut-o↵ artifacts as the coarse restorations are pasted at higher resolutions. We start by studying this phenomenon on a simple DCT pyramid, for which the artifacts resulting from this process are evident. We propose a simple solution consisting of a "conservative recomposition" of the scales that only retains the lower frequencies of each scale, with the obvious exception of the scale at the highest resolution. This soft fusion eliminates the ringing artifacts and attenuates staircasing artifacts and low frequency bumps. An added benefit of the DCT pyramid is that it allows to maintain the noise white at the lower resolutions, hence can be combined with any denoising algorithm without adaptation. This soft fusion recipe can be generalized to any other pyramid structure. We apply it to a Laplacian pyramid as an example. Our proposal merges and operates any denoising algorithm into a multi-scale method, with improvements both in visual quality and PSNR, and with little additional complexity. The method is demonstrated on several classic or state-of-the-art denoising algorithms. Note to referees: This article has an IPOL companion paper describing thoroughly the proposed method applied to DCT denoising

This paper presents DA3D (Data Adaptive Dual Domain Denoising), a "last step denoising" method that takes as input a noisy image and as a guide the result of any state-of-the-art denoising algorithm. The method performs frequency domain shrinkage on shape and data-adaptive patches. Unlike other dual denoising methods, DA3D doesn't process all the image samples, which allows it to use large patches (64 × 64 pixels). The shape and data-adaptive patches are dynamically selected, effectively concentrating the computations on areas with more details, thus accelerating the process considerably. DA3D also reduces the staircasing artifacts sometimes present in smooth parts of the guide images.The effectiveness of DA3D is confirmed by extensive experimentation. DA3D improves the result of almost all state-of-the-art methods, and this improvement requires little additional computation time.

This article presents DA3D (Data Adaptive Dual Domain Denoising), a "last step denoising" method that takes as input a noisy image and as a guide the result of any state-of-the-art denoising algorithm. The method performs frequency domain shrinkage on shape and dataadaptive patches. DA3D doesn't process all the image samples, which allows it to use large patches (64 × 64 pixels). The shape and data-adaptive patches are dynamically selected, effectively concentrating the computations on areas with more details, thus accelerating the process considerably. DA3D also reduces the staircasing artifacts sometimes present in smooth parts of the guide images. The effectiveness of DA3D is confirmed by extensive experimentation. DA3D improves the result of almost all state-of-the-art methods, and this improvement requires little additional computation time. Source CodeThe C++ source code, the code documentation, and the online demo are accessible at the IPOL web page of this article web site 1 Compilation and usage instruction are included in the README.txt file of the archive.