Optimization

Hello, could you help me with parts A and B? ADMM stands for Alternating Direction Method of Multipliers.

Consider imgmat, a 31 X 31 sparse image, in which 620 of the 961 pixels have a value of 0. You can think of this image as a toy version of an MRI image that we are interested in collecting. Suppose that, because of the nature of the machine that collects the MRI image, it takes a long time to measure each pixel value individually, but it is faster to measure linear combinations of pixel values. The machine produces three batches of 150 linear combinations, with the weights in the linear combination being random. Additionally, since the machine is not perfect, noise is added to the linear combinations. In mathematical notation, we have 961 J'o' = Z xop'p + Go P=1 where xii-p ~ N(0,1) are the random weights, ,6}, is the vectorized image, E\" ~ NULZS) is the measurement noise, 1' = 1,2,3,j = 1,m,15{l andp = 1,~-,961. The observed values y\