The research of effective and reliable detrending methods for Spitzer data is of paramount importance for the characterization of exoplanetary atmospheres. To date, the totality of exoplanetary observations in the mid-and farinfrared, at wavelengths >3 μm, have been taken with Spitzer. In some cases, in past years, repeated observations and multiple reanalyses of the same data sets led to discrepant results, raising questions about the accuracy and reproducibility of such measurements. Morello et al. (2014Morello et al. ( , 2015 proposed a blind-source separation method based on the Independent Component Analysis of pixel time series (pixel-ICA) to analyze InfraRed Array Camera (IRAC) data, obtaining coherent results when applied to repeated transit observations previously debated in the literature. Here we introduce a variant to the pixel-ICA through the use of wavelet transform, wavelet pixel-ICA, which extends its applicability to low-signal-to-noise-ratio cases. We describe the method and discuss the results obtained over 12 eclipses of the exoplanet XO3b observed during the "Warm Spitzer" era in the 4.5 μm band. The final results are reported, in part, also in Ingalls et al. ), which appeared on arXiv while this paper was under review. Based on many statistical tests discussed in Ingalls et al. (2016), the wavelet pixel-ICA method performs as well as or better than other state-of-art methods recently developed by other teams to analyze Spitzer/IRAC data, and, in particular, it appears to be the most repeatable and the most reliable, while reaching the photon noise limit, at least for the particular data set analyzed. Another strength of the ICA approach is its highest objectivity, as it does not use prior information about the instrument systematics, making it a promising method to analyze data from other observatories. The selfconsistency of individual measurements of eclipse depth and phase curve slope over a span of more than three years proves the stability of Warm Spitzer/IRAC photometry within the error bars, at the level of 1 part in 10 4 in stellar flux.