Related papers: On Finite Alphabet Compressive Sensing

The goal of compressed sensing is to reconstruct a sparse signal under a few linear measurements far less than the dimension of the ambient space of the signal. However, many real-life applications in physics and biomedical sciences carry…

Recent works have shown that tokenisation is NP-complete. However, these works assume tokenisation is applied to inputs with unboundedly large alphabets -- an unrealistic assumption, given that in practice tokenisers operate over fixed-size…

We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…

Machine learning has had a major impact on data compression over the last decade and inspired many new, exciting theoretical and applied questions. This paper describes one such direction -- relative entropy coding -- which focuses on…

The past several years have witnessed a surge of research investigating various aspects of sparse representations and compressed sensing. Most of this work has focused on the finite-dimensional setting in which the goal is to decompose a…

Recent results in compressed sensing show that, under certain conditions, the sparsest solution to an underdetermined set of linear equations can be recovered by solving a linear program. These results either rely on computing sparse…

It is essential for a robot to be able to detect revisits or loop closures for long-term visual navigation.A key insight explored in this work is that the loop-closing event inherently occurs sparsely, that is, the image currently being…

In engineered quantum systems, the Hamiltonian is often not completely known and needs to be determined experimentally with accuracy and efficiency. We show that this may be done at temperatures that are greater than the characteristic…

Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that,…

Tensor completion is a natural higher-order generalization of matrix completion where the goal is to recover a low-rank tensor from sparse observations of its entries. Existing algorithms are either heuristic without provable guarantees,…

We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…

Compressive sensing has been successfully used for optimized operations in wireless sensor networks. However, raw data collected by sensors may be neither originally sparse nor easily transformed into a sparse data representation. This…

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…

Suffixient sets are a novel prefix array (PA) compression technique based on subsampling PA (rather than compressing the entire array like previous techniques used to do): by storing very few entries of PA (in fact, a compressed number of…

In compressed sensing a sparse vector is approximately retrieved from an under-determined equation system $Ax=b$. Exact retrieval would mean solving a large combinatorial problem which is well known to be NP-hard. For $b$ of the form…

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an…

Compressed sensing in MRI enables high subsampling factors while maintaining diagnostic image quality. This technique enables shortened scan durations and/or improved image resolution. Further, compressed sensing can increase the diagnostic…

Text indexing is a classical algorithmic problem that has been studied for over four decades: given a text $T$, pre-process it off-line so that, later, we can quickly count and locate the occurrences of any string (the query pattern) in $T$…

Data compression is very important feature in terms of saving the memory space. In this proposal, an indexed dictionary based compression is used for text data, where the word's reference in dictionary is used for compression. This approach…