A GPU-based fast solution method for L1 minimization problem

Abstract

The invention provides a GPU-based L1 minimization problem fast solving method. A CUDA parallel computation model is utilized on a NVIDIA Maxwell-architecture GPU device, and an L1 minimization problem fast solving method is provided by utilizing GPU new features and internal kernel merging and optimizing technologies. According to the GPU-based L1 minimization problem fast solving method, not only designs of self-adaptation optimal vector computation, non-transposed matrix vector multiplication and transposed matrix vector multiplication are included, but also parallel solving of single or parallel multiple L1 minimization problems can be implemented only by simple CUDA thread allocation configuration difference. Based on experimental results, the GPU-based L1 minimization problem fast solving method provided by the invention is efficient, and also has high parallelism and adaptability. Compared with the existing parallel solving method, the GPU-based L1 minimization problem fast solving method has largely improved performances.

Description

technical field [0001] The invention relates to the fields of signal processing and face recognition, and more specifically relates to a GPU-based fast solution method for L1 minimization problem. Background technique [0002] The L1 minimization problem is min||x|| 1 , satisfying the constraint Ax=b, where A∈R m×n (m<<n) is a dense matrix of full rank, b∈R m is a preset vector, x∈R n is an unknown solution. The solution of the L1 minimization problem, also known as sparse representation, has been widely used in many fields, such as signal processing, machine learning and statistical inference, etc. To solve the L1 minimization problem, researchers have designed many effective algorithms. For example, gradient projection method, truncated Newton interior point method, homotopy method, iterative shrinkage threshold method and augmented Lagrangian multiplier method, etc. In practice, b often contains noise, so a variant of this problem is called the unconstrained b...

AI Technical Summary

Problems solved by technology

However, through testing, it is found that the matrix-vector multiplication method in CUBLAS will produce performance fluctuations as the number of matrix rows or columns increases, and the maximum and minimum performance gaps are significant.

CUBLAS does not support Fusion. When facing multiple concurrent L1 minimization problems, it cannot make full use of the new features of the existing GPU, and cannot optimally configure the computing resources of the entire GPU, resulting in large additional overhead.

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