Exploiting Inter-pixel Coherence II

Let’s come back to the discussion on compressive sensing applied to light transport problem. We will talk about two approaches to exploit inter-pixel coherence today.

• The first is described to in the paper Compressive Light Transport Sensing by Peers et al. (Link)
• The second is a recent technical report(?) titled Adaptive compressed image sensing based on wavelet modeling and direct sampling by Deutsch, Averbuch, and Dekel. (Link)

What these two approaches have in common is their use of hierarchical basis, wavelets in particular. Computation in both papers proceeds from one involving coarse wavelet coefficients to one involving finer coefficients, and the result of the coarser level is used to “bootstrap” the computation of the finer level.

Tensor unfolding with numpy

We switch gear to some easy programming today. Let’s write a routine to unfold a tensor. We’ll use numpy to store tensor as it’s the only linear algebra library that features multi-dimentional array.

Exploiting Inter-pixel Coherence

Recall the measurement equation from last time:

Suppose again that the responses of the pixels to each light source are coherent. That is, we may hope that there is a basis such that the columns of are sparse. Then, we have that

or