3D GPU-based implementation of the contrast source inversion for breast lesion detection

In microwave tomography, applying a proper inversion method to the measured data may result in quantitative imaging of the electrical properties (EPs) at the frequencies of the used electromagnetic radiation. Some physiopathological statuses of the breast tissue can be distinguished based on the estimated EPs [1]. A previous approach presented in [2] reports preliminary results obtained with a two-dimensional implementation of the Contrast Source Inversion (CSI) method [3] applied to simulated data. This work aims to discuss the transition to a 3D algorithm. Some optimization techniques in the MATLAB environment have been applied to the 2D version to reduce time consumption, which becomes a predominant variable with 3D data. Namely, computationally expensive operations on large data have been transferred to GPU (NVIDIA A 100 80 GB). This leads to an advantage especially for the FFT, which is performed in every iterative step. The efforts have permitted to reduce the execution time of each iterative step, reaching a speed-up factor of about 25 with respect to the CPU (Intel Xeon Gold 6430 2.10 GHz 512 GB RAM) version of the code. To obtain preliminary results about the feasibility of the 3D imaging method for detecting dielectric properties, a virtual experiment was performed. The transmit-receive setup is composed of a transmitting antenna that assumes ten equidistant positions around a cylindrical phantom, and a receiving antenna assuming forty equidistant positions around it. A heterogeneous phantom was considered, with electrical properties that emulate the ones of a healthy breast (σ = 0.1 and εr = 4), and a longitudinal cylindrical inclusion (r = 1 cm), whose high electrical properties simulate those of a breast lesion (σ = 1 and εr = 15). The incident electric field was obtained through the simulation of a Hom antenna fed at the frequency of 5 GHz, performed in Sim4Life. Total electric fields were computed in the receiving antennas’ locations and a homogeneous initial guess (σ = 0.01 and εr = 3) was adopted. An additive regularization in the CSI cost functional was introduced to overcome the image artifacts induced by the ill-posedness of the inverse scattering problem. Figure 1 provides results obtained after 3,000 iterations of CSI (about 2.5 hours of execution).