Can ICA be applied, when the number of mixture signal is less than number of source signal? I am referring to the the following paper : Non-contact, automated cardiac pulse measurements using video imaging and blind source separation

In the above article, the authors are able to extract cardiac pulse signal out from RGB components. I try to visualize the process as follow.

R' = R + cardiac pulse
G' = G + cardiac pulse
B' = B + cardiac pulse


R', G' and B' are the colour components observed by camera. R, G, B are the colour components for a person, by assuming that he doesn't have any cardiac pulse.

It seems that we will be having 4 sources (R, G, B, Cardiac pulse). We are now trying to obtain 1 of the 4 sources (Cardiac pulse) from 3 mixture signals (R', G', B'), by using ICA.

Does it make sense? Am I missing some techniques? Or, am I making a wrong assumption on the process?
You are making a wrong assumption on the process. In ICA, the number of mixtures must be at least as many as the number of components. The paper you cite does in fact, acknowledge this:


  These observed signals from the red, green and blue color sensors are denoted by $x_1(t)$, $x_2(t)$ and $x_3(t)$ respectively, which are amplitudes of the recorded signals (averages of all pixels in the facial region) at time point $t$. In conventional ICA the number of recoverable sources cannot exceed the number of observations, thus we assumed three underlying source signals, represented by $s_1(t)$, $s_2(t)$ and $s_3(t)$.


The conversion $x_i^'=(x_i-\mu_i)/\sigma_i$ is merely centering and sphering of the data, which I explain in another answer on this site.



The cases considered in the paper are the noiseless ICA model and noisy ICA. In other words, the heart rate measurements considered at rest (not a pulseless model as you suggested) is the ICA model:

$$\mathbf{x}(t)=\mathbf{As}(t)$$

where $\mathbf{x}$ is the observed vector, $\mathbf{s}$ is the underlying component vector and $\mathbf{A}$ is the mixing matrix. 

On the other hand, heart rate measurements when in motion can be considered as

$$\mathbf{x}(t)=\mathbf{As}(t)+\mathbf{n}(t)$$

where $\mathbf{n}(t)$ is a noise vector (in this case the motions).