A Combinatorial Approach to Quantitative Microwave Imaging for Breast Tumour Profiling Using SVBIM and SpaRSA
Thathamkulam A. Anjit
A combinatorial quantitative reconstruction method employing Subspace-based Virtual Born Iteration Method (SVBIM) along with a greedy compressive sensing algorithm, Sparse Reconstruction by Separable Approximation (SpaRSA) to solve the ill-posed inverse problem in microwave imaging is proposed in this paper. SVBIM makes use of the contribution of the variational induced current to arrive at a better estimate of the permittivity profile in each iteration. SpaRSA operates in the sparse domain and reduces the computational overload, thereby guiding the inverse problem towards a faster global optimum solution. The merger of these two algorithms helps to reconstruct breast profiles having high-permittivity tumour inclusions (ε = 60) with reduced error. The proposed reconstruction method is capable of extracting the salient information regarding tissue differentiation (permittivity and conductivity) and dielectric distribution of various tumour and fibroglandular inclusions within the object, dimensions, resolution, size, shape and coordinate localization of inclusions. In comparison to various methods reported in literature, the results obtained using the proposed method are highly encouraging. In the presence of 30 dB noise, the above-said imaging technique produces a significantly reduced permittivity error value of 0.47 in the reconstruction of tumour inclusions as against 0.85 and 0.71 in the case of TV norm and Re-weighted Basis Pursuit methods respectively. The experimental validation is carried out using a phantom having three inclusions of sizes 10 mm, 6 mm, and 3 mm. The inclusions have been localized successfully with errors of 0.089, 0.133, and 0.21, respectively.