Related papers: On the Uniqueness of Group Sparse Coding

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…

Sparse coding has achieved a great success in various image processing tasks. However, a benchmark to measure the sparsity of image patch/group is missing since sparse coding is essentially an NP-hard problem. This work attempts to fill the…

Sparse coding (SC) is attracting more and more attention due to its comprehensive theoretical studies and its excellent performance in many signal processing applications. However, most existing sparse coding algorithms are nonconvex and…

Sparse superimposed coding (SSC) has emerged as a promising technique for short-packet transmission in ultra-reliable low-latency communication scenarios. However, conventional SSC schemes often suffer from high encoding and decoding…

We investigate group coding for arbitrary finite groups acting linearly on a vector space. These yield robust codes based on real or complex matrix groups. We give necessary and sufficient conditions for correct subgroup decoding using…

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…

High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing…

In the short block length regime, ensemble decoding schemes with their inherently parallel structure can improve error correction performance and reduce latency compared to stand-alone suboptimal decoders such as belief propagation (BP). In…

Sparse coding (SC) is an automatic feature extraction and selection technique that is widely used in unsupervised learning. However, conventional SC vectorizes the input images, which breaks apart the local proximity of pixels and destructs…

Sparse coding is a basic task in many fields including signal processing, neuroscience and machine learning where the goal is to learn a basis that enables a sparse representation of a given set of data, if one exists. Its standard…

Inspired by recent work on convex formulations of clustering (Lashkari & Golland, 2008; Nowozin & Bakir, 2008) we investigate a new formulation of the Sparse Coding Problem (Olshausen & Field, 1997). In sparse coding we attempt to…

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…

Special functions, coding theory and $t$-designs have close connections and interesting interplay. A standard approach to constructing $t$-designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the…

In this paper, we analyze the uniqueness of the sparse time frequency decomposition and investigate the efficiency of the nonlinear matching pursuit method. Under the assumption of scale separation, we show that the sparse time frequency…

Sparse coding has achieved a great success in various image processing studies. However, there is not any benchmark to measure the sparsity of image patch/group because sparse discriminant conditions cannot keep unchanged. This paper…

Block encoding of sparse matrices underpins powerful quantum algorithms such as quantum singular value transformation, Hamiltonian simulation, and quantum linear solvers, yet its efficient gate-level realization for general sparse matrices…

We prove an Assmus-Mattson-type theorem for block codes where the alphabet is the vertex set of a commutative association scheme (say, with $s$ classes). This in particular generalizes the Assmus-Mattson-type theorems for…

All current popular hand-crafted key-point detectors such as Harris corner, MSER, SIFT, SURF... rely on some specific pre-designed structures for the detection of corners, blobs, or junctions in an image. In this paper, a novel sparse…

In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance…

Algebraic Subspace Clustering (ASC) is a simple and elegant method based on polynomial fitting and differentiation for clustering noiseless data drawn from an arbitrary union of subspaces. In practice, however, ASC is limited to…