Related papers: On Random Construction of a Bipolar Sensing Matrix…
Energy and direction are tow basic properties of a vector. A discrete signal is a vector in nature. RIP of compressive sensing can not show the direction information of a signal but show the energy information of a signal. Hence, RIP is not…
We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our…
Parallel imaging with linear predictability takes advantage of information present in multiple receive coils to accurately reconstruct the image with fewer samples. Commonly used algorithms based on linear predictability include GRAPPA and…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below…
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, properties of natural signals are…
An algebraic investigation on bicomplex numbers is carried out here. Particularly matrices and linear maps defined on them are discussed. A new kind of cartesian product, referred to as an idempotent product, is introduced and studied. The…
The bigraph theory is a relatively young, yet formally rigorous, mathematical framework encompassing Robin Milner's previous work on process calculi, on the one hand, and provides a generic meta-model for complex systems such as multi-agent…
We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
The polarization properties of perfectly periodical and defective one-dimensional photonic bandgap structures with nonreciprocal chiral (bi-isotropic) layers are studied. The method of solution is based on the 2x2-block-representation…
In this paper we formulate and prove a statistical version of the Candes-Tao restricted isometry property (SRIP for short) which holds in general for any incoherent dictionary which is a disjoint union of orthonormal bases. In addition, we…
Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function…
Boolean functions can be used to construct binary linear codes in many ways, and vice versa. The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the…
A number of ill-posed inverse problems in signal processing, like blind deconvolution, matrix factorization, dictionary learning and blind source separation share the common characteristic of being bilinear inverse problems (BIPs), i.e. the…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…