Large amounts of deep optical images will be available in the near future, allowing statistically significant studies of low surface brightness structures such as intracluster light (ICL) in galaxy clusters. The detection of these structures requires efficient algorithms dedicated to this task, where traditional methods suffer difficulties. We present our new Detection Algorithm with Wavelets for Intracluster light Studies (DAWIS), developed and optimised for the detection of low surface brightness sources in images, in particular (but not limited to) ICL. DAWIS follows a multiresolution vision based on wavelet representation to detect sources, embedded in an iterative procedure called synthesis-by-analysis approach to restore the complete unmasked light distribution of these sources with very good quality. The algorithm is built so sources can be classified based on criteria depending on the analysis goal; we display in this work the case of ICL detection and the measurement of ICL fractions. We test the efficiency of DAWIS on 270 mock images of galaxy clusters with various ICL profiles and compare its efficiency to more traditional ICL detection methods such as the surface brightness threshold method. We also run DAWIS on a real galaxy cluster image, and compare the output to results obtained with previous multiscale analysis algorithms. We find in simulations that in average DAWIS is able to disentangle galaxy light from ICL more efficiently, and to detect a greater quantity of ICL flux due to the way it handles sky background noise. We also show that the ICL fraction, a metric used on a regular basis to characterise ICL, is subject to several measurement biases both on galaxies and ICL fluxes. In the real galaxy cluster image, DAWIS detects a faint and extended source with an absolute magnitude two orders brighter than previous multiscale methods.
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