Landweber Iterative Algorithm

The Landweber iterative algorithm is an iterative class algorithm used for Electrical Capacitance Tomography (ECT) image reconstruction. This algorithm is widely applied in medical fields, employing a step-by-step iterative approach to reconstruct capacitance tomography images. In this algorithm, image reconstruction is achieved by continuously updating pixel values of the image to approximate the true image. The Landweber method typically implements this through gradient descent optimization, where each iteration updates the image matrix using the formula: x_k+1 = x_k + αA^T(b - Ax_k), where A represents the sensitivity matrix, b is the measured capacitance vector, and α denotes the relaxation parameter controlling convergence rate. Key advantages of the Landweber iterative algorithm include its simplicity and reliability, making it one of the commonly used algorithms in the field of electrical capacitance tomography. Implementation typically involves setting appropriate stopping criteria (maximum iterations or error threshold) and optimizing the relaxation parameter for stable convergence.