The choice of an appropriate frame, or dictionary, is a crucial step in the sparse representation of a given class of signals. Traditional dictionary learning techniques generally lead to unstructured dictionaries that are costly to deploy and train, and do not scale well to higher dimensional signals. In order to overcome such limitation, we propose a learning algorithm that constrains the dictionary to be a sum of Kronecker products of smaller subdictionaries. This approach, named sum of Kronecker products, is demonstrated experimentally in an image denoising application.

Accurate crop type mapping using satellite imagery is crucial for food security, yet accurately distinguishing between crops with similar spectral signatures is challenging. This study assessed the performance of Sentinel-2 (S2) time series (spectral bands and vegetation indices), Sentinel-1 (S1) time series (backscattering coefficients and polarimetric parameters), alongside phenological features derived from both S1 and S2 time series (harmonic coefficients and median features), for classifying sunflower, soybean, and maize. Random Forest (RF), Multi-Layer Perceptron (MLP), and XGBoost classifiers were applied across various dataset configurations and train-test splits over two study sites and years in France. Additionally, the InceptionTime classifier, specifically designed for time series data, was tested exclusively with time series datasets to compare its performance against the three general machine learning algorithms (RF, XGBoost, and MLP). The results showed that XGBoost outperformed RF and MLP in classifying the three crops. The optimal dataset for mapping all three crops combined S1 backscattering coefficients with S2 vegetation indices, with comparable results between phenological features and time series data (mean F1 scores of 89.9% for sunflower, 76.6% for soybean, and 91.1% for maize). However, when using individual satellite sensors, S1 phenological features and time series outperformed S2 for sunflower, while S2 was superior for soybean and maize. Both phenological features and time series data produced close mean F1 scores across spatial, temporal, and spatiotemporal transfer scenarios, though median features dataset was the best choice for spatiotemporal transfer. Polarimetric S1 data did not yield effective results. The InceptionTime classifier further improved classification accuracy over XGBoost for all crops, with the degree of improvement varying by crop and dataset (the highest mean F1 scores of 90.6% for sunflower, 86.0% for soybean, and 93.5% for maize).

Accurate crop type information is of paramount importance for decision makers. This paper focuses on refining rapeseed field detection. This goal is achieved by creating high accuracy rapeseed maps using Sentinel-1 (S1) time series and secondly, by developing different solutions for mapping the rapeseed fields when there are constraints in ground samples collection. Proposed solutions include transferring a model developed over one year to other years with no re-training, and developing models with limited training samples. The research evaluates the performance of Random Forest (RF) and three deep learning (DL) algorithms: Long Short-Term Memory Fully Convolutional Network (LSTM-FCN), InceptionTime, and Multi-layer Perceptron (MLP). All four algorithms were used to classify the S1 time series with a large number of ground samples from the same years for training and testing. Smaller sample sizes were then tested for the training phase (100, 300, 500 and 1000 samples in a study site of 800 km2). Model transferability is tested across years. The impact of S1 image count on transfer accuracy is examined. Additionally, the effect of the phenological shift in the rapeseed growth cycle of 15 and 30 days between the training and test years was also investigated. The findings demonstrate strong model performance when training and testing occur in the same year (F1-score up to 95%). Within sample sizes of 300 to 1000, RF and InceptionTime stand out with high accuracy (F1-score>90%). When employing different years for training and testing with ample sample sizes, all four algorithms correctly classified rapeseed (F1-score between 85.5% and 92.7%). In cases of a reduced number of images, the performance of InceptionTime and LSTM-FCN decreased (16% decrease in the F1-score), while RF and MLP maintain their performance. Notably, RF outperforms DL algorithms with an F1 score of 89.1%. In the context of a phenological shift, only InceptionTime and LSTM-FCN demonstrated strong performance (F1-score between 87.7% and 92.6%).

This study investigates the potential of Sentinel-1 (S1) multi-temporal data for the early-season mapping of the rapeseed crop. Additionally, we explore the effectiveness of limiting the portion of a considered time series to map rapeseed fields. To this end, we conducted a quantitative analysis to assess several temporal windows (periods) spanning different phases of the rapeseed phenological cycle in the following two scenarios relating to the availability or constraints of providing ground samples for different years: (i) involving the same year for both training and the test, assuming the availability of ground samples for each year; and (ii) evaluating the temporal transferability of the classifier, considering the constraints of ground sampling. We employed two different classification methods that are renowned for their high performance in land cover mapping: the widely adopted random forest (RF) approach and a deep learning-based convolutional neural network, specifically the InceptionTime algorithm. To assess the classification outcomes, four evaluation metrics (recall, precision, F1 score, and Kappa) were employed. Using S1 time series data covering the entire rapeseed growth cycle, the tested algorithms achieved F1 scores close to 95% on same-year training and testing, and 92.0% when different years were used, both algorithms demonstrated robust performance. For early rapeseed detection within a two-month window post-sowing, RF and InceptionTime achieved F1 scores of 67.5% and 77.2%, respectively, and 79.8% and 88.9% when extended to six months. However, in the context of temporal transferability, both classifiers exhibited mean F1 scores below 50%. Notably, a 5-month time series, covering key growth stages such as stem elongation, inflorescence emergence, and fruit development, yielded a mean F1 score close to 95% for both algorithms when trained and tested in the same year. In the temporal transferability scenario, RF and InceptionTime achieved mean F1 scores of 92.0% and 90.0%, respectively, using a 5-month time series. Our findings underscore the importance of a concise S1 time series for effective rapeseed mapping, offering advantages in data storage and processing time. Overall, the study establishes the robustness of RF and InceptionTime in rapeseed detection scenarios, providing valuable insights for agricultural applications.

In this paper, we propose a way to combine two acceleration techniques for the ℓ ₁ -regularized least squares problem: safe screening tests, which allow to eliminate useless dictionary atoms; and the use of fast structured approximations of the dictionary matrix. To do so, we introduce a new family of screening tests, termed stable screening, which can cope with approximation errors on the dictionary atoms while keeping the safety of the test (i.e., zero risk of rejecting atoms belonging to the solution support). Some of the main existing screening tests are extended to this new framework. The proposed algorithm consists in using a coarser (but faster) approximation of the dictionary at the initial iterations and then switching to better approximations until eventually adopting the original dictionary. A systematic switching criterion based on the duality gap saturation and the screening ratio is derived. Simulation results show significant reductions in both computational complexity and execution times for a wide range of tested scenarios.