Hyperspectral images are typically composed of hundreds of narrow and contiguous spectral bands, each containing information regarding the material composition of the imaged scene. However, these images can be affected by various sources of noise, distortions, or data loss, which can significantly degrade their quality and usefulness. This paper introduces a convergent guaranteed algorithm, LRS-PnP-DIP(1-Lip), which successfully addresses the instability issue of DHP that has been reported before. The proposed algorithm extends the successful joint low-rank and sparse model to further exploit the underlying data structures beyond the conventional and sometimes restrictive unions of subspace models. A stability analysis guarantees the convergence of the proposed algorithm under mild assumptions , which is crucial for its application in real-world scenarios. Extensive experiments demonstrate that the proposed solution consistently delivers visually and quantitatively superior inpainting results, establishing state-of-the-art performance.

Hyperspectral imaging (HSI) is a key technology for earth observation, surveillance, medical imaging and diagnostics, astronomy and space exploration. The conventional technology for HSI in remote sensing applications is based on the push-broom scanning approach in which the camera records the spectral image of a stripe of the scene at a time, while the image is generated by the aggregation of measurements through time. In real-world airborne and spaceborne HSI instruments, some empty stripes would appear at certain locations, because platforms do not always maintain a constant programmed attitude, or have access to accurate digital elevation maps (DEM), and the travelling track is not necessarily aligned with the hyperspectral cameras at all times. This makes the enhancement of the acquired HS images from incomplete or corrupted observations an essential task. We introduce a novel HSI inpainting algorithm here, called Hyperspectral Equivariant Imaging (Hyper-EI). Hyper-EI is a self-supervised learning-based method which does not require training on extensive datasets or access to a pre-trained model. Experimental results show that the proposed method achieves state-of-the-art inpainting performance compared to the existing methods.

In recent years, self-supervised learning has excelled for its capacity to learn robust feature representations from unlabelled data. Networks pretrained through self-supervision serve as effective feature extractors for downstream tasks, including Few-Shot Learning. While the evaluation of unsupervised approaches for few-shot learning is well-established in imagery, it is notably absent in acoustics. This study addresses this gap by assessing large-scale self-supervised models' performance in few-shot audio classification. Additionally, we explore the relationship between a model's few-shot learning capability and other downstream task benchmarks. Our findings reveal state-of-the-art performance in some few-shot problems such as SpeechCommandsv2, as well as strong correlations between speech-based few-shot problems and various downstream audio tasks.

Hyperspectral Image (HSI)s cover hundreds or thousands of narrow spectral bands, conveying a wealth of spatial and spectral information. However, due to the instrumental errors and the atmospheric changes, the HSI obtained in practice are often contaminated by noise and dead pixels(lines), resulting in missing information that may severely compromise the subsequent applications. We introduce here a novel HSI missing pixel prediction algorithm, called Low Rank and Sparsity Constraint Plug-and-Play (LRS-PnP). It is shown that LRS-PnP is able to predict missing pixels and bands even when all spectral bands of the image are missing. The proposed LRS-PnP algorithm is further extended to a self-supervised model by combining the LRS-PnP with the Deep Image Prior (DIP), called LRS-PnP-DIP. In a series of experiments with real data, It is shown that the LRS-PnP-DIP either achieves state-of-the-art inpainting performance compared to other learning-based methods, or outperforms them.

Hyperspectral images are typically composed of hundreds of narrow and contiguous spectral bands, each containing information about the material composition of the imaged scene. However, these images can be affected by various sources of noise, distortions, or data losses, which can significantly degrade their quality and usefulness. To address these problems, we introduce two novel self-supervised Hyperspectral Images (HSI) inpainting algorithms: Low Rank and Sparsity Constraint Plug-and-Play (LRS-PnP), and its extension LRS-PnP-DIP, which features the strong learning capability, but is still free of external training data. We conduct the stability analysis under some mild assumptions which guarantees the algorithm to converge. It is specifically very helpful for the practical applications. Extensive experiments demonstrate that the proposed solution is able to produce visually and qualitatively superior inpainting results, achieving state-of-the-art performance. The code for reproducing the results is available at \url{https://github.com/shuoli0708/LRS-PnP-DIP}.

Contrastive self-supervised learning has gained attention for its ability to create high-quality representations from large unlabelled data sets. A key reason that these powerful features enable data-efficient learning of downstream tasks is that they provide augmentation invariance, which is often a useful inductive bias. However, the amount and type of invariances preferred is not known apriori, and varies across different downstream tasks. We therefore propose a multi-task self-supervised framework (MT-SLVR) that learns both variant and invariant features in a parameter-efficient manner. Our multi-task representation provides a strong and flexible feature that benefits diverse downstream tasks. We evaluate our approach on few-shot classification tasks drawn from a variety of audio domains and demonstrate improved classification performance on all of them

Non-negative signals form an important class of sparse signals. Many algorithms have already beenproposed to recover such non-negative representations, where greedy and convex relaxed algorithms are among the most popular methods. The greedy techniques are low computational cost algorithms, which have also been modified to incorporate the non-negativity of the representations. One such modification has been proposed for Matching Pursuit (MP) based algorithms, which first chooses positive coefficients and uses a non-negative optimisation technique that guarantees the non-negativity of the coefficients. The performance of greedy algorithms, like all non-exhaustive search methods, suffer from high coherence with the linear generative model, called the dictionary. We here first reformulate the non-negative matching pursuit algorithm in the form of a deep neural network. We then show that the proposed model after training yields a significant improvement in terms of exact recovery performance, compared to other non-trained greedy algorithms, while keeping the complexity low.

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As this model is often unknown for many classes of the signals, we need to select such a model based on the domain knowledge or using some exemplar signals. This paper presents a new exemplar based approach for the linear model (called the dictionary) selection, for such sparse inverse problems. The problem of dictionary selection, which has also been called the dictionary learning in this setting, is first reformulated as a joint sparsity model. The joint sparsity model here differs from the standard joint sparsity model as it considers an overcompleteness in the representation of each signal, within the range of selected subspaces. The new dictionary selection paradigm is examined with some synthetic and realistic simulations.