Image denoising with a non-monotone boosted DCA for non-convex models

Image reconstruction is important for activities that rely on optical and comparative data analysis. Signals obtained through acquisition systems can be inconsistent due to several factors, such as camera movement and noise, but they can be modeled mathematically. With this, continuous optimization tools have become popular in recent years for image problems. This work seeks to reconstruct noisy images using a non -monotone boosted DC algorithm (nmBDCA), an accelerated variant of the Difference of Convex Algorithm (DCA), with a non-convex version of the total variation (TV) model, to obtain better computational performance than DCA and superior quality of the restored image. Specifically, the performance of the non-convex TV model is compared to its convex formulation. Two sections of experiments are included, one with black-and-white images and another with grayscale medical computed tomography (CT) images. The results of the first section emphasize that nmBDCA performs reconstructions with higher PSNR in all experiments, lower CPU time, and SSIM greater or equal to DCA in 91.67% of tests. The non-convex TV model is more robust than the convex one in the presence of more noise, presenting higher SSIM and PSNR in all experiments performed. In the section of experiments with CT images, nmBDCA outperforms DCA in reconstruction quality and CPU time in all tests performed. The performance of the non-convex model applied with nmBDCA outperforms the convex model in SSIM and CPU time in all experiments, being superior in PSNR in 77.78% of the tests.