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In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from a lower dimensional linear measurement vector. Typically it is assumed that the decoder has access to the encoder matrix, which in the combinatorial case is sparse and binary. In this paper we consider the problem of designing a decoder to recover a set of sparse codes from their linear measurements alone, that is without access to encoder matrix. To this end we study the matrix factorisation task of recovering both the encoder and sparse coding matrices from the associated linear measurement matrix. The contribution of this paper is a computationally efficient decoding algorithm, Decoder-Expander Based Factorisation, with strong performance guarantees. In particular, under mild assumptions on the sparse coding matrix and by deploying a novel random encoder matrix, we prove that Decoder-Expander Based Factorisation recovers both the encoder and sparse coding matrix at the optimal measurement rate with high probability and from a near optimal number of measurement vectors. In addition, our experiments demonstrate the efficacy and computational efficiency of our algorithm in practice. Beyond compressed sensing our results may be of interest for researchers working in areas such as linear sketching, coding theory and matrix compression.
A reinforcement-learning-based non-uniform compressed sensing (NCS) framework for time-varying signals is introduced. The proposed scheme, referred to as RL-NCS, aims to boost the performance of signal recovery through an optimal and adaptive distrib
In applications of scanning probe microscopy, images are acquired by raster scanning a point probe across a sample. Viewed from the perspective of compressed sensing (CS), this pointwise sampling scheme is inefficient, especially when the target imag
We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements and emph{a
A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the generator t
The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual physical implemen