The block-wise circumcentered–reflection method

A Block-Wise random sampling approach: Compressed sensing problem

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initiali...

Block-wise Alternating Direction Method of Multipliers with Gaussian Back Substitution for Multiple-block Convex Programming

We consider the linearly constrained convex minimization model with a separable objective function which is the sum of m functions without coupled variables, and discuss how to design an efficient algorithm based on the fundamental technique of splitting the augmented Lagrangian method (ALM). Our focus is the specific big-data scenario where m is huge. A pretreatment on the original data is to ...

Block-wise Alternating Direction Method of Multipliers for Multiple-block Convex Programming and Beyond

The alternating direction method of multipliers (ADMM) is a benchmark for solving a linearly constrained convex minimization model with a two-block separable objective function; and it has been shown that its direct extension to a multiple-block case where the objective function is the sum of more than two functions is not necessarily convergent. For the multipleblock case, a natural idea is to...

Block-Wise Non-Malleable Codes

Non-malleable codes, introduced by Dziembowski, Pietrzak, and Wichs (ICS ’10) provide the guarantee that if a codeword c of a message m, is modified by a tampering function f to c′, then c′ either decodes to m or to “something unrelated” to m. It is known that non-malleable codes cannot exist for the class of all tampering functions and hence a lot of work has focused on explicitly constructing...

Object Tracking via Pixel-Wise and Block-Wise Sparse Representation