2019/08/16 by Mohammed Rayyan Sheriff, Debasish Chatterjee, Sheriff, Mohammed Rayyan +1
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #cs.LG #eess.SP #electronic engineering #information engineering #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1908.06065
openalex publication_date 2019/08/16 · arxiv created 2020/01/08 · arxiv updated 2020/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from its relatively few random linear measurements. Such problems arise in variety of settings with applications ranging from medical image processing, recommender systems etc. We provide an exposition to the convex duality of the linear inverse problems, and obtain a novel and equivalent convex-concave min-max reformulation that gives rise to simple ascend-descent type algorithms to solve an LIP. Moreover, such a reformulation is crucial in developing methods to solve the dictionary learning problem with almost sure recovery constraints.