Improvement of the total focusing method using an inverse problem approach

Imaging using the total focusing method (TFM) is a popular tool, which is becoming a standard, for nondestructive testing and evaluation. From full matrix capture data, it consists in focusing at each point of a defined reconstruction zone. It is generally more efficient than conventional phased array focusing, which only focuses at a few points. Despite its good image quality, TFM suffers from a lack of resolution and contrast, in particular in the case of close defects or in scattering materials. The TFM algorithm can be formalized as a linear operation on the data. The contribution of this paper is then to include a sparsity-inducing penalization to the TFM procedure. The reconstructed image is therefore supposed to contain only a few non zero values, corresponding to flaws or geometry. The final image is obtained by minimizing a penalized least-squares criterion within an iterative procedure. A first example uses data acquired from two close side drilled holes (SDH) in an aluminum block. The proposed algorithm shows good echo separation whereas the reference method suffers from overlapping, demonstrating resolution improvement. A second example comes from a stainless steel specimen, with high scattering noise level. The proposed method reduces the scattering noise and improves the contrast.