This work presents a series of computational experiments to evaluate the performance and convergence of various iterative methods for solving a minimization problem \(\begin{aligned}&\min _{{\textbf {x}} \in \mathbb {R}^{n}} \Vert {\textbf {x}}\Vert _2\nonumber \\&\text {subject to} \; {\textbf {A}} {\textbf {x}}={\textbf {b}}, \end{aligned}\) where \( {\textbf {A}} \in \mathbb {R}^{m \times n}\; (m \le n)\) ( \( {\textbf {A}} \) is full row rank) and \( {\textbf {b}} \in \mathbb {R}^{m}\) are known and \( {\textbf {x}} \in \mathbb {R}^{n} \) must be determined. The proposed methods are compared with Craig’s method, and the direct pseudo-inverse approach using MATLAB. The efficiency of these methods is assessed based on the convergence behavior and CPU time required for each iteration. Numerical results for different problem sizes indicate that one of the new methods achieves the fastest convergence and lowest computational cost. The effectiveness of these methods is also demonstrated through an image face decryption example. Finally a minimum-norm steganography method is proposed for covert message transmission using digital images. By solving a constrained optimization problem, a secret message is securely embedded and transmitted through the image, and experimental results confirm accurate decoding and high imperceptibility.
