Since tree roots are important to ecosystems, particularly in the context of global climate change, better understanding their organization is necessary. Ground-penetrating radar (GPR) appears a useful tool to that effect. In this contribution, a novel processing procedure to reconstruct 3D root architectures from GPR data in heterogeneous environments is proposed, involving three main steps: (i) noise-related information is removed using Singular Value Decomposition (SVD), (ii) a modified version of Randomized Hough Transform (RHT) yields the soil dielectric constant, (iii) a matched filter technique combined with Hilbert Transform then operates as wave migration. Viability is first studied from comprehensive numerical simulations carried out with gprMax software on a realistic root model in a 3D heterogeneous environment. The heterogeneous soil effect is studied carefully through a number of simulations involving six different soil types. Then, controlled laboratory measurements are conducted on a root prototype using a bi-static GPR system involving folded complementary bowtie antennas in the 300 MHz to 3.3 GHz frequency range. 3D results from both simulations and experiments show the good performance and potential of the proposed processing.