Zero-order-hold for two dimensional signal $x(t_1,t_2)$ From Wikipedia:


  A zero-order hold reconstructs the following continuous-time waveform
  from a sample sequence $x[n]$, assuming one sample per time interval
  $T$: $$x_{\mathrm{ZOH}}(t)\,= \sum_{n=-\infty}^{\infty} x[n]\cdot
 \mathrm{rect} \left(\frac{t-T/2 -nT}{T} \right) \ $$ where
  $\mathrm{rect}()$  is the rectangular function.


We can refer to $\mathrm{rect}()$ also as one-dimensional rectangular function. For example, the product of two one-dimensional rect functions can be viewed as a rect function in two dimension, i.e. a function
that has the value 1 on the square of side length 1 centered at the origin, and has the value 0 outside this
square. I am wondering if there exists, for example, a two dimensional version of ZOH for a signal in two variable, $x(t_1,t_2)$.

Thanks in advance.
Yes there exists a 2D analog of the 1D zero order hold for image reconstruction, whose mathematical formulation follows closely that of 1D case as:
$$I_{\mathrm{ZOH}}(x,y)\,= \sum_{n=-\infty}^{\infty} \sum_{m=-\infty}^{\infty} x[n,m]\cdot \operatorname{rect} \left( {x-nT_x,y-mT_y} \right) $$

Where $x[n,m]$ is the spatial samples of 2D image to be reconstructed, $T_x$ and $T_y$ are sampling periods in $x$ and $y$ dimensions (which are generally equal in practice) and the $\operatorname{rect}()$ function is a 2D rectengular pulse of height one and durations $T_x$ and $T_y$ along the dimensions.

The zero order hold interpolation can easily be observed when you enlarge an image through an image editor by not using any smooth interpolation methods but just repeated filling of those new enlarged pixels. 

In particular just use, for example, IrfanView to open any image and choose Image->Resize from menu, then choose to enlarge the image from the options in the coming window, and finally choose "Resize (faster, lo quality)" option from the "Size Methods" sections about lower right corner (for version 4.40)

If you instead choose "smooth" methods, they will fill in the pixels with calculated intermediate values, therefore implementing higher order holds than zero.