<p>The reduced biquaternion matrix equation has significant applicaitions in color image restoration. This study addresses the least squares symmetric solution, the pure imaginary least squares symmetric solution and the pure real least squares symmetric solution through an innovative integration of the real representation of the reduced biquaternion matrix and the <i>H</i>-representation of the symmetric matrix. A novel methodology is developed to obtain the necessary and sufficient conditions for the existence of these solutions using the Moore-Penrose generalized inverse. Subsequently, corresponding algorithms are proposed to demonstrate the feasibility and effectiveness of the method in numerical experiments. Notably, compared with the traditional complex representation method, the novel method achieves better experimental results in terms of CPU time. Furthermore, when it is applied to solve color image restoration problem, this method shows excellent visual effect and high restoration quality.</p>