Sparse modulation for robust signaling and synchronization

A non-transitory computer readable medium comprising instructions stored therein that, when executed by one or more processors, cause said one or more processors to perform the following acts:

• defining a 2D synchronization signal in a spatial-frequency domain;
• applying an NM×NM inverse Fourier transform to said signal, to yield an NM×NM array of sync signal values in a spatial domain;
• logically combining said NM×NM array of sync signal values with an N×N array of variable data, wherein each datum of variable data corresponds to an M×M sub-block of sync signal values, yielding an NM×NM array of composite values defining a pattern;
• in an M×M sub-block within said NM×NM array of composite values, identifying a first set of P elements as candidates for darkening, wherein said identifying comprises determining the P elements whose values are most extreme among said M×M sub-block from the array of composite values;
• and
• producing a pattern including a second set of P elements that are darkened for printing.

An apparatus comprising:

• an input for receiving variable data;
• one or more electronic processors configured for:
• defining a 2D synchronization signal in a spatial-frequency domain;
• applying an NM×NM inverse Fourier transform to said signal, to yield an NM×NM array of sync signal values in a spatial domain;
• logically combining said NM×NM array of sync signal values with an N×N array of variable data, wherein each datum of variable data corresponds to an M×M sub-block of sync signal values, yielding an NM×NM array of composite values defining a pattern;
• in an M×M sub-block within said NM×NM array of composite values, identifying a first set of P elements as candidates for darkening, wherein said identifying comprises determining the P elements whose values are most extreme among said M×M sub-block from the array of composite values;
• producing a pattern including a second set of P elements that are darkened for printing;
• and
• an output for outputting the pattern.