<p>A family of descent spectral three-term conjugate gradient methods is introduced in which the coefficient of the third term is determined by approaching its search direction to the memoryless DFP (Davidon–Fletcher–Powell) update. In addition, the spectral parameter is computed in such a way as to ensure the sufficient descent condition for the general objective functions. The convergence analysis is discussed under standard assumptions for nonconvex optimization problems. Moreover, the complexity analysis is established under the Armijo line search strategy. The practical merits of the proposed algorithm are computationally demonstrated on a set of CUTEr test functions as well as the nonnegative matrix factorization problem. To strengthen the numerical results from a practical point of view, further experiments are conducted on the well-known image restoration problem as a real-world case study. Finally, a summarized analysis of the outputs is provided, which mainly demonstrates the practical advantages of the suggested algorithm.</p>