This paper presents an iterative image reconstruction algorithm based on the minimization of the total variation (TV) for divergent-beam computed tomography (CT). The algorithm is designed to handle insufficient data problems, such as few-view projections, limited-angle scans, and detector bin gaps, which are common in practical CT applications. The TV algorithm is shown to be effective in reconstructing accurate images from sparse or insufficient data, even when standard analytic algorithms like filtered back-projection (FBP) produce artifacts. The TV algorithm is based on the assumption that the gradient of the image is sparse, which is often the case in tomographic images. The algorithm minimizes the TV of the image, which is defined as the sum of the magnitudes of the image gradients. This approach is particularly useful for images that are relatively constant over large regions but have rapid variations at boundaries. The TV algorithm is implemented using a combination of gradient descent and projection on convex sets (POCS) to enforce the constraints of the projection data. The algorithm is tested on various scenarios, including few-view projections, limited-angle scans, and bad detector bins. The results show that the TV algorithm produces images that are visually indistinguishable from the true image, even when the data are sparse or inconsistent. The algorithm is also compared with standard iterative algorithms like the expectation-maximization (EM) and algebraic reconstruction technique (ART), which are known to be sensitive to data inconsistencies. The TV algorithm is found to be more robust and efficient, requiring fewer iterations to achieve accurate results. The paper also discusses the application of the TV algorithm to different types of CT imaging, including fan-beam and cone-beam CT. The algorithm is shown to be effective in handling the challenges of divergent-beam CT, where the central slice theorem cannot be used to transform the projection data into the image's Fourier space. The TV algorithm is able to reconstruct accurate images from sparse data, even when the data are not sufficient for exact reconstruction. The algorithm is also shown to be robust to noise and other inconsistencies in the data, making it a promising approach for practical CT applications.This paper presents an iterative image reconstruction algorithm based on the minimization of the total variation (TV) for divergent-beam computed tomography (CT). The algorithm is designed to handle insufficient data problems, such as few-view projections, limited-angle scans, and detector bin gaps, which are common in practical CT applications. The TV algorithm is shown to be effective in reconstructing accurate images from sparse or insufficient data, even when standard analytic algorithms like filtered back-projection (FBP) produce artifacts. The TV algorithm is based on the assumption that the gradient of the image is sparse, which is often the case in tomographic images. The algorithm minimizes the TV of the image, which is defined as the sum of the magnitudes of the image gradients. This approach is particularly useful for images that are relatively constant over large regions but have rapid variations at boundaries. The TV algorithm is implemented using a combination of gradient descent and projection on convex sets (POCS) to enforce the constraints of the projection data. The algorithm is tested on various scenarios, including few-view projections, limited-angle scans, and bad detector bins. The results show that the TV algorithm produces images that are visually indistinguishable from the true image, even when the data are sparse or inconsistent. The algorithm is also compared with standard iterative algorithms like the expectation-maximization (EM) and algebraic reconstruction technique (ART), which are known to be sensitive to data inconsistencies. The TV algorithm is found to be more robust and efficient, requiring fewer iterations to achieve accurate results. The paper also discusses the application of the TV algorithm to different types of CT imaging, including fan-beam and cone-beam CT. The algorithm is shown to be effective in handling the challenges of divergent-beam CT, where the central slice theorem cannot be used to transform the projection data into the image's Fourier space. The TV algorithm is able to reconstruct accurate images from sparse data, even when the data are not sufficient for exact reconstruction. The algorithm is also shown to be robust to noise and other inconsistencies in the data, making it a promising approach for practical CT applications.