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Cosmic voids and their corresponding redshift-projected mass densities, known as troughs, play an important role in our attempt to model the large-scale structure of the Universe. Understanding these structures enables us to compare the standard model with alternative cosmologies, constrain the dark energy equation of state, and distinguish between different gravitational theories. In this paper, we extend the subspace-constrained mean shift algorithm, a recently introduced method to estimate density ridges, and apply it to 2D weak lensing mass density maps from the Dark Energy Survey Y1 data release to identify curvilinear filamentary structures. We compare the obtained ridges with previous approaches to extract trough structure in the same data, and apply curvelets as an alternative wavelet-based method to constrain densities. We then invoke the Wasserstein distance between noisy and noiseless simulations to validate the denoising capabilities of our method. Our results demonstrate the viability of ridge estimation as a precursor for denoising weak lensing observables to recover the large-scale structure, paving the way for a more versatile and effective search for troughs.