This paper presents a new box-constrained multiplicative iterative (BCMI) algorithm for image restoration under box constraints. The algorithm is designed to handle image restoration problems where pixel values are constrained within a finite range, such as 8-bit images with values in [0, 255]. The BCMI algorithm avoids the need for matrix inversion and active set identification, making it computationally efficient. It is applied to TV (total variation) image restoration problems with Poisson, Gaussian, and salt-and-pepper noise. The algorithm is proven to be globally convergent under certain conditions and is shown to produce better restorations than existing methods in simulation studies. The BCMI algorithm is implemented with pixel-wise updates and incorporates a line search strategy to ensure convergence. The algorithm is tested on various noise models and is shown to achieve higher signal-to-noise ratios (PSNR) compared to other methods like FISTA, projected FTVD, and projected TVAL. The results demonstrate that box constraints improve restoration quality, especially for images with many pixels near the dynamic range limits. The algorithm is efficient and easy to implement, making it suitable for a wide range of image restoration tasks.This paper presents a new box-constrained multiplicative iterative (BCMI) algorithm for image restoration under box constraints. The algorithm is designed to handle image restoration problems where pixel values are constrained within a finite range, such as 8-bit images with values in [0, 255]. The BCMI algorithm avoids the need for matrix inversion and active set identification, making it computationally efficient. It is applied to TV (total variation) image restoration problems with Poisson, Gaussian, and salt-and-pepper noise. The algorithm is proven to be globally convergent under certain conditions and is shown to produce better restorations than existing methods in simulation studies. The BCMI algorithm is implemented with pixel-wise updates and incorporates a line search strategy to ensure convergence. The algorithm is tested on various noise models and is shown to achieve higher signal-to-noise ratios (PSNR) compared to other methods like FISTA, projected FTVD, and projected TVAL. The results demonstrate that box constraints improve restoration quality, especially for images with many pixels near the dynamic range limits. The algorithm is efficient and easy to implement, making it suitable for a wide range of image restoration tasks.