## 4 Quantum and Classical Image-Processing Algorithms
### Compressive Sensing  
In order to reduce the amount of required data (at present \(10^{3}\)-\(10^{4}\) frames) by at least one order of magnitude, we are exploring different approaches. First, we are investigating the opportunity of implementing compression techniques for improving bus bandwidth utilization, thus acting on data transfer optimization. Data compression may also rely on manipulation of raw input data to determine only the relevant information in a sort of information bottleneck paradigm, in which software nodes in a lattice provide their \begin{table}
\begin{tabular}{c c} \hline \hline  & **Jetson Xavier AGX** \\ \hline GPU & 512-core NVIDIA VoltaTM GPU with 64 Tensor Cores \\ CPU & 8-core NVIDIA Carmel ArmWv8.2 64-bit CPU 8 MB L2 + 4 MB L3 \\ Memory & 16 GB 256-bit LPDDR4x 136.5 GB/s \\ PCIE & \(1\times 8+1\times 4+1\times 2+2\times 1\) (PCIe Gen4, Root Port \& Endpoint) \\ DL Accelerator & 2\(\times\) NVDLA Engines \\ Vision Accelerator & 7-Way VLIW Vision Processor \\ Connectivity & 10/100/1000 BASE-T Ethernet \\ \hline \hline \end{tabular}
\end{table} 
Table 1: NVIDIA Jetson Xavier AGX: Technical Specifications. Figure 5: Qu3D scenario for GPU parallel processing based on NVIDIA Volta architecture as provided by an NVIDIA Jetson AGX Xavier device. contribution to a probable reconstruction of the actual decompressed data. This is very similar to artificial neural network structures, where the network stores a representation of a phenomenon and returns a response based on some similarity rating versus the observed data. Moreover, the availability of advanced processing technologies allows the investigation and implementation of alternative techniques able to exploit the sparsity of the retrieved signal to reconstruct information from a heavily sub-sampled signal, by compressive sensing techniques [46; 47]. As in other correlation imaging techniques, such as ghost imaging (GI), in the CPI protocol, the object image is reconstructed by performing correlation measurements between intensities at two disjoint detectors. [PERSON] et al. [48] demonstrated that conventional GI offers the possibility to perform compressive sensing (CS) boosting the recovered image quality. CS theory asserts the possibility of recovering the object image from far fewer samples than required by the Nyquist-Shannon sampling theorem, and it relies on two main principles: sparsity of the signal (once expressed in a proper basis) and incoherence between the sensing matrix and the sparsity basis. In conventional GI, the transmission measured for each speckle pattern represents a projection of the object image and CS finds the sparsest image among all the possible images consistent with the projections. In practice, CS reconstruction algorithms solve a convex optimization problem, looking for the image which minimizes the \(L_{1}-\)norm in the sparse basis among the ones compatible with the bucket measurements, see Refs. [49; 50; 51; 52] for a review. We are developing a novel protocol reducing the number of measurements required for image recovery by an order of magnitude. Once properly refocused, a single acquisition can be fed into the compressive sensing algorithm several times thus exploiting the plenoptic properties of the acquired data and increasing the signal-to-noise ratio of the final refocused image. We tested the CS-CPI algorithm with numerical simulations, as summarized in Figure 6. In (a), a double-slit mask is reconstructed by correlations measurements considering \(N=6000\) frames; in (b), the standard reconstruction is repeated considering only the 10% of available frames, while, in (c), the CS reconstruction using the same reduced set of measured data. In addition to a data-fidelity term corresponding to a linear regression, we penalized the \(L_{1}-\)norm of the reconstructed image to account for its sparsity in the \(2D-DCT\) domain. The resulting optimization problem is known as the LASSO (Least Absolute Shrinkage and Selection Operator) [53].