A projection-domain iterative algorithm for metal artifact reduction by minimizing the total-variation norm and the negative-pixel energy

Morphing from the TV-Norm to the l 0 -Norm

For piecewise constant objects, the images can be reconstructed with under-sampled measurements. The gradient image of a piecewise image is sparse. If a sparse solution is a desired solution, anl 0 -norm minimization method is effective to solve an under-determined system. However, thel 0 -norm is not differentiable, and it is not straightforward to minimize anl 0 -norm. This paper suggests a function that is like thel 0 -norm function, and we refer to this function as metal 0 -norm. The subdifferential of the metal 0 -norm has a simple explicit expression. Thus, it is straightforward to derive a gradient descent algorithm to enforce the sparseness in the solution. In fact, the proposed meta norm is a transition that varies between the TV-norm and thel 0 -norm. As an application, this paper uses the proposed metal 0 -norm for few-view tomography. Computer simulation results indicate that the proposed metal 0 -norm effectively guides the image reconstruction algorithm to a piecewise constant solution. It is not clear whether the TV-norm or thel 0 -norm is more effective in producing a sparse solution. Index Terms-Inverse problem, optimization, total-variation minimization,l 0 -norm minimization, few-view tomography, iterative algorithm, image reconstruction.

Application of computer image processing technology in old artistic design restoration

Art designs exhibit different principles, textures, color combinations, and creative skills for vivid thinking visualizations. Art exhibits are far from ages, periods, and creators finding their digital patterns in recent years for resurrection. Degraded periodic artworks are digitally handled for reviving their legacy using digital image processing. This article introduces Textural Restoration Technique (TRT) using Deep Feature Processing (DFP) to augment such innovations. The proposed technique analyses the tampered image for its textures, and available features are extracted. The textures are expected to be sequential based on gradient distribution; the missing gradients are identified from the available features near the region of interest (ROI). The ROI is marked by combining missing and available features from which textural edges are sketched. In this process, recurrent learning is employed for verifying the gradient substitutions for even textures. The texture patterns are classified using high and low accuracy features exhibited between two successive ROIs. First, the learning model is trained using gradient distribution accuracy pursued by the texture completion edge. The second training is pursued by the first distribution, achieving the maximum restoration. The filled features and their gradient positions are marked by moving the ROIs for distinguishing textures. The restoration ratio is computed with high accuracy based on the filled edges.