  As the availability of imagery data continues to swell, so do the demands on
transmission, storage and processing power. Processing requirements to handle
this plethora of data is quickly outpacing the utility of conventional
processing techniques. Transitioning to quantum processing and algorithms that
offer promising efficiencies over conventional methods can address some of
these issues. However, to make this transformation possible, fundamental issues
of implementing real time Quantum algorithms must be overcome for crucial
processes needed for intelligent analysis applications. For example, consider
edge detection tasks which require time-consuming acquisition processes and are
further hindered by the complexity of the devices used thus limiting
feasibility for implementation in real-time applications. Convolution is
another example of an operation that is essential for signal and image
processing applications, where the mathematical operations consist of an
intelligent mixture of multiplication and addition that require considerable
computational resources. This paper studies a new paired transform-based
quantum representation and computation of one-dimensional and 2-D signals
convolutions and gradients. A new visual data representation is defined to
simplify convolution calculations making it feasible to parallelize convolution
and gradient operations for more efficient performance. The new data
representation is demonstrated on multiple illustrative examples for quantum
edge detection, gradients, and convolution. Furthermore, the efficiency of the
proposed approach is shown on real-world images.
