Deep Learning (DL) is one of many successful methodologies to extract informative patterns and insights from ever increasing noisy large-scale datasets (in our case, satellite images). However, DL models consist of a few thousand to millions of training parameters, and these training parameters require tremendous amount of electrical power for extracting informative patterns from noisy large-scale datasets (e.g., computationally expensive). Hence, we employ a quantum-inspired tensor network for compressing trainable parameters of physics-informed neural networks (PINNs) in Earth science. PINNs are DL models penalized by enforcing the law of physics; in particular, the law of physics is embedded in DL models. In addition, we apply tensor decomposition to HyperSpectral Images (HSIs) to improve their spectral resolution. A quantum-inspired tensor network is also the native formulation to efficiently represent and train quantum machine learning models on big datasets on GPU tensor cores. Furthermore, the key contribution of this paper is twofold: (I) we reduced a number of trainable parameters of PINNs by using a quantum-inspired tensor network, and (II) we improved the spectral resolution of remotely-sensed images by employing tensor decomposition. As a benchmark PDE, we solved Burger’s equation. As practical satellite data, we employed HSIs of Indian Pine, USA and of Pavia University, Italy.

Causality is one of the most important topics in a Machine Learning (ML) research, and it gives insights beyond the dependency of data points. Causality is a very vital concept also for investigating the dynamic surface of our living planet. However, there are not many attempts for integrating a causal model in Remote Sensing (RS) methodologies. Hence, in this paper, we propose to use patch-based RS images and to represent each patch-based image by a single variable (e.g. entropy). Then we use a Structural Equation Model (SEM) to study their cause-effect relation. Moreover, the SEM is a simple causal model characterized by a Directed Acyclic Graph (DAG). Its nodes are causal variables, and its edges represent causal relationships among causal variables if and only if causal variables are dependent.

Machine Learning (ML) techniques are employed to analyze and process big Remote Sensing (RS) data, and one well-known ML technique is a Support Vector Machine (SVM). An SVM is a quadratic programming (QP) problem, and a D-Wave quantum annealer (D-Wave QA) promises to solve this QP problem more efficiently than a conventional computer. However, the D-Wave QA cannot solve directly the SVM due to its very few input qubits. Hence, we use a coreset ("core of a dataset") of given EO data for training an SVM on this small D-Wave QA. The coreset is a small, representative weighted subset of an original dataset, and any training models generate competitive classes by using the coreset in contrast to by using its original dataset. We measured the closeness between an original dataset and its coreset by employing a Kullback-Leibler (KL) divergence measure. Moreover, we trained the SVM on the coreset data by using both a D-Wave QA and a conventional method. We conclude that the coreset characterizes the original dataset with very small KL divergence measure. In addition, we present our KL divergence results for demonstrating the closeness between our original data and its coreset. As practical RS data, we use Hyperspectral Image (HSI) of Indian Pine, USA

This letter studies how to program and assess a parameterized quantum circuit (PQC) for classifying Earth observation (EO) satellite images. In this exploratory study, we assess a PQC for classifying a two-label EO image dataset and compare it with a classic deep learning classifier. We use the PQC with an input space of only 17 quantum bits (qubits) due to the current limitations of quantum technology. As a real-world image for EO, we selected the Eurosat dataset obtained from multispectral Sentinel-2 images as a training dataset and a Sentinel-2 image of Berlin, Germany, as a test image. However, the high dimensionality of our images is incompatible with the PQC input domain of 17 qubits. Hence, we had to reduce the dimensionality of the input images for this two-label case to a vector with 16 elements; the 17th qubit remains reserved for storing label information. We employed a very deep convolutional network with an autoencoder as a technique for the dimensionality reduction of the input image, and we mapped the dimensionally reduced image onto 16 qubits by means of parameter thresholding. Then, we used a PQC to classify the two-label content of the dimensionally reduced Eurosat image dataset. A PQC classifies the Eurosat images with high accuracy as a classic deep learning method (and with even better accuracy in some instances). From our experiment, we derived and enhanced deeper insight into programming future gate-based quantum computers for many practical problems in EO.

Quantum algorithms are designed to process quantum data (quantum bits) in a gate-based quantum computer. They are proven rigorously that they reveal quantum advantages over conventional algorithms when their inputs are certain quantum data or some classical data mapped to quantum data. However, in a practical domain, data are classical in nature, and they are very big in dimension, size, and so on. Hence, there is a challenge to map (embed) classical data to quantum data, and even no quantum advantages of quantum algorithms are demonstrated over conventional ones when one processes the mapped classical data in a gate-based quantum computer. For the practical domain of earth observation (EO), due to the different sensors on remote-sensing platforms, we can map directly some types of EO data to quantum data. In particular, we have polarimetric synthetic aperture radar (PolSAR) images characterized by polarized beams. A polarized state of the polarized beam and a quantum bit are the Doppelganger of a physical state. We map them to each other, and we name this direct mapping anatural embedding, otherwise anartificial embedding. Furthermore, we process ournaturally embeddeddata in a gate-based quantum computer by using a quantum algorithm regardless of its quantum advantages over conventional techniques; namely, we use the QML network as a quantum algorithm to prove that wenaturally embeddedour data in input qubits of a gate-based quantum computer. Therefore, we employed and directly processed PolSAR images in a QML network. Furthermore, we designed and provided a QML network with an additional layer of a neural network, namely, a hybrid quantum-classical network, and demonstrate how to program (via optimization and backpropagation) this hybrid quantum-classical network when employing and processing PolSAR images. In this work, we used a gate-based quantum computer offered by an IBM Quantum and a classical simulator for a gate-based quantum computer. Our contribution is that we provided very specific EO data with anatural embeddingfeature, the Doppelganger of quantum bits, and processed them in a hybrid quantum-classical network. More importantly, in the future, these PolSAR data can be processed by future quantum algorithms and future quantum computing platforms to obtain (or demonstrate) some quantum advantages over conventional techniques for EO problems.

The Markov Random Field (MRF) is used for extracting feature information in images and is formed as an Ising-like model. The quantum annealing is a novel method to optimize objective functions, and objective functions have to be expressed in terms of the Ising model. Hence, the MRF can be embedded into the the quantum annealing method, and feature information of remote sensing images then can be extracted using a quantum annealing computer. Extracted information or features are used to segment an image.