The variable projection method has been developed as a powerful tool for solvingseparable nonlinear least squares problems. It has proven effective in cases where the underlying model consists of a linear combination of nonlinear functions, such as exponential functions. In this thesis, a modified version of the variable projection method to address a challenging semi-blind deconvolution problem involving mixed Gaussian kernels is employed. The aim is to recover the original signal accurately while estimating the mixed Gaussian kernel utilized during the convolution process. The numerical results obtained through the implementation of the proposed algo- rithm are presented. These results highlight the method’s ability to approximate the true signal successfully. However, accurately estimating the mixed Gaussian kernel remains a challenging task. The implementation details, specifically focusing on con- structing a simplified Jacobian for the Gauss-Newton method, are explored. This contribution enhances the understanding and practicality of the approach.