Help in problem formulation for estimation of image as a feature vector - SISO or MIMO FIR channel model? Based on the paper Blind Image deconvolution:

A feature vector is a list of numbers used to represent an image. The feature vector for my case takes values as symbols $-1,1$. 

An instance or an example of an image is represented as a feature vector of $d$ feature values $\mathbf{x} = [x_1,x_2,...,x_d]$. I have $N$ examples 
$$\{\mathbf{x}_i\}_{i=1}^N$$ in the form of a database. So, the database contains $N$ rows of feature vectors each of $d$ length.  One such pattern (feature vector) is 
$$\mathbf{x} =  [1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1]'$$
where $d = 30$ 
The database thus has $N$ rows of examples each of $d$ length :
$$ \mathbf{x_1} = x_{11},x_{12},....,x_{1d}$$
$$ \mathbf{x_2} = x_{21},x_{22},....,x_{2d}$$
$$ ::$$
$$ \mathbf{x_N} = x_{N1},x_{N2},....,x_{Nd}$$

I don't know how to use the above as input to the channel. In general,
the output is, 
$$\mathbf{y} = H^T x$$

Assuming that the impulse response is that of FIR, then I am facing difficulty in how to represent the channel. Should the source input be each component of the feature vector or an entire example?


if the input in the form of the feature vector is transmitted via a channel whose impulse response is modeled as moving average (finite response, FIR) then inputs and how many outputs should there be? The output would be the convolution of the input and the impulse response. Would the channel be Single input-Single Output FIR or Multiple Input Multiple Output FIR ? The objective is to estimate the channel parameters and the input using estimation methods from the output observation only. Would the estimation be performed using one example or all the examples?  
Should there be $d$ channel coefficients?
A mathematical representation of the system will really help to clear the concept. Thank you
This question is confusing, but I thought I'd try to make some sense of it.

Suppose you are transmitting one of your $\mathbf{x}_i$ vectors one component at a time. That is, the transmitted signal, $s[k]$,  for the $i^{\rm th}$ feature vector is:
$$
s_i[k] = x_{ik}
$$
If this signal is corrupted by a channel with impulse response $h[k]$ then the received signal, $y[k]$ will be
$$
y[k] = h[k] \star s_i[k] = \sum_{m=0}^{M-1} h[m] s_i[k-m] = \sum_{m=0}^{M-1} h[m] x_{im}
$$
where $\star$ represents convolution.

If we use this formulation, then the answer to:


  Should the source input be each component of the feature vector or an entire example?


is that it should be each component of the feature vector.


  if the input in the form of the feature vector is transmitted via a channel whose impulse response is modeled as moving average (finite response, FIR) then inputs and how many outputs should there be?


There should be a sequence of outputs. If the FIR filter is length $M$, then the output will be of length $M+d-1$.


  Would the channel be Single input-Single Output FIR or Multiple Input Multiple Output FIR ? 


In the model above, it is a SISO system.


  Would the estimation be performed using one example or all the examples?


If the channel does not change, then you might be better off using all the data you have available.


  Should there be $d$ channel coefficients?


There is no point in tying the number of feature vector components with the length of the channel. In the above, the length of the channel is $M$.