vim-1 : Estimation of model parameters

Hi, I am trying to construct the encoding model described in "Identifying natural images from human brain activity" . 

I have some questions about the "Estimation of model parameters”:

1) For each voxel the DC offset is defined as: c (1 x 1) but the final estimate ĉ = ỹ - Xμ ĥ has dimension (p x 1). How is that possible? 

2) When I have evaluated the final estimate of the kernel ĥ for one voxel (for example in V1) I have noticed that there is not sparsity, so there are few weights for every     voxel (the weights are distributed over the whole image). In that way, starting from one voxel it is not possible to reconstruct a part of the image as I expected but the whole one. Does this make sense?

Best regards.