Spectral Conjugate Gradient Like Method for Signal Reconstruction
Abdulkarim Hassan Ibrahim, Kanikar Muangchoo, Auwal Bala Abubakar, Afeez Dewumi Adedokun, Hassan Mohammed
Abstract
This paper presents a derivative-free conjugate gradient algorithm for solving the $l_1$-regularization problem arising in compressive sensing. The search direction of the proposed method is bounded and satisfies the sufficient descent condition. Under some mild assumptions, the global convergence of the proposed algorithm is established. Numerical experiments in recovering sparse signal are performed to illustrate the efficiency of the algorithm compared with existing algorithms.
Topics & Concepts
Conjugate gradient methodMathematicsNonlinear conjugate gradient methodRegularization (linguistics)Gradient descentDerivation of the conjugate gradient methodConvergence (economics)AlgorithmBounded functionConjugateGradient methodConjugate residual methodCompressed sensingDescent (aeronautics)Signal reconstructionApplied mathematicsSIGNAL (programming language)Mathematical optimizationSignal processingMathematical analysisComputer scienceArtificial intelligenceArtificial neural networkEconomic growthProgramming languageRadarEngineeringTelecommunicationsAerospace engineeringEconomicsSparse and Compressive Sensing TechniquesNumerical methods in inverse problemsPhotoacoustic and Ultrasonic Imaging