  We present a comprehensive analysis of the performance of noise-reduction
(``denoising'') algorithms to determine whether they provide advantages in
source detection on extragalactic survey images. The methods under analysis are
Perona-Malik filtering, Bilateral filter, Total Variation denoising,
Structure-texture image decomposition, Non-local means, Wavelets, and
Block-matching. We tested the algorithms on simulated images of extragalactic
fields with resolution and depth typical of the Hubble, Spitzer, and Euclid
Space Telescopes, and of ground-based instruments. After choosing their best
internal parameters configuration, we assess their performance as a function of
resolution, background level, and image type, also testing their ability to
preserve the objects fluxes and shapes. We analyze in terms of completeness and
purity the catalogs extracted after applying denoising algorithms on a
simulated Euclid Wide Survey VIS image, on real H160 (HST) and K-band (HAWK-I)
observations of the CANDELS GOODS-South field. Denoising algorithms often
outperform the standard approach of filtering with the Point Spread Function
(PSF) of the image. Applying Structure-Texture image decomposition,
Perona-Malik filtering, the Total Variation method by Chambolle, and Bilateral
filtering on the Euclid-VIS image, we obtain catalogs that are both more pure
and complete by 0.2 magnitudes than those based on the standard approach. The
same result is achieved with the Structure-Texture image decomposition
algorithm applied on the H160 image. The advantage of denoising techniques with
respect to PSF filtering increases at increasing depth. Moreover, these
techniques better preserve the shape of the detected objects with respect to
PSF smoothing. Denoising algorithms provide significant improvements in the
detection of faint objects and enhance the scientific return of current and
future extragalactic surveys.
