Related papers: Adaptive sensing using deterministic partial Hadam…
In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted…
We study compressed sensing when the sampling vectors are chosen from the rows of a unitary matrix. In the literature, these sampling vectors are typically chosen randomly; the use of randomness has enabled major empirical and theoretical…
The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…
In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi information dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we…
This paper presents an improved analysis of a structured dimension-reduction map called the subsampled randomized Hadamard transform. This argument demonstrates that the map preserves the Euclidean geometry of an entire subspace of vectors.…
Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: $(i)$ Estimate latent variables…
The field of compressed sensing has become a major tool in high-dimensional analysis, with the realization that vectors can be recovered from relatively very few linear measurements as long as the vectors lie in a low-dimensional structure,…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically…
We present an incremental, scalable and efficient dimension reduction technique for tensors that is based on sparse random linear coding. Data is stored in a compactified representation with fixed size, which makes memory requirements low…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
Compressed sensing is the art of reconstructing structured $n$-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytic reconstruction guarantees support this credo. The strongest among them…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…
This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian…
This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy…
A Hadamard-Hitchcock decomposition of a multidimensional array is a decomposition that expresses the latter as a Hadamard product of several tensor rank decompositions. Such decompositions can encode probability distributions that arise…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
As a typical dimensionality reduction technique, random projection can be simply implemented with linear projection, while maintaining the pairwise distances of high-dimensional data with high probability. Considering this technique is…