An alternative method using a machine learning (ML) algorithm is presented for the reconstruction of the plasma radiation profile (plasma radiation power profile in a poloidal cross-section) from the foil image of the infrared imaging video bolometer (IRVB). In the data analysis of the IRVB, the plasma radiation profile cannot be directly converted from the foil image of the IRVB, while the projection matrix constructing the foil image from the plasma radiation profile is easily derived from the geometric structure of the system. That is, there is no inverse matrix of the projection matrix. So, the Phillips-Thikhonov (P-T) algorithm is widely used for the reconstruction of the plasma profile. Here an alternative method is proposed, and this method directly finds the pseudo-inverse matrix of the projection matrix of the IRVB using the ML algorithm. The two algorithms have been examined in an impurity injection experiment. Our alternative algorithm is found to have advantages in the reconstruction of detailed features when compared with the P-T algorithm.