Tomographic Image Deblurring Using Steepest Descent

Abstract

In the course of image reconstruction, pixel values can scatter in a diverse way (e.g., speckling, diffraction and diffusion). Speckle is a kind of scattering that leads towards blur. Speckled signal values swing from high to low in concerned pixel. Speckle is not a random error. It removed by further processing of image using suitable deconvolution technique. The digitalization of the problem leads towards linear equations of an ill-posed matrix --- Krylov operator such as steepest descent useful tool to handle such situations. The methods discussed in this paper are modified residual norm steepest descent (MRNSD) and conjugate gradient for least-square problems (CGLS). These two techniques variation of steepest descent, hence the iterative algorithm in nature. Like many other iterative algorithms, these two practices suffer from semi-convergence. This paper focus on the deblurring of image reconstructed from the received data in industrial tomography along-with effective way to tackle semi-convergence.