Image Denoising and Reconstruction

This lecture covers the process of denoising gray scale images by minimizing the sum of the Frobenius norm of the noisy image and a total variation regularization term. It also discusses the reconstruction of color images by filling in missing pixels using total variation minimization. The instructor demonstrates the equivalence of the denoising problem to a second-order cone program and provides insights on choosing the regularization weight for optimal denoising. Practical examples include denoising a noisy image of a dog and reconstructing the Mona Lisa image. The lecture concludes with a discussion on the visual effects of different regularization strengths in image reconstruction.