title: An Lp(0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint.
abstract: BACKGROUND
  In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research regarding constructing and optimizing objective functions. However, although these algorithms dramatically improved reconstruction images, few of them have designed an essentially differentiable objective function whose full gradient is easy to obtain to accelerate the optimization process.
  
  
  METHODS
  This paper introduces a new kind of non-negative prior information, designing differentiable objective functions for cases of L1-norm, Lp(0 < p < 1)-norm and L0-norm. Incorporating this non-negative prior information, it is easy to obtain the gradient of these differentiable objective functions, which is useful to guide the optimization process.
  
  
  RESULTS
  Performance analyses are conducted using both numerical and phantom experiments. In terms of spatial resolution, quantitativeness, gray resolution and execution time, the proposed methods perform better than the conventional regularization methods without this non-negative prior information.
  
  
  CONCLUSIONS
  The proposed methods improves the reconstruction images using the introduced non-negative prior information. Furthermore, the non-negative constraint facilitates the gradient computation, accelerating the minimization of the objective functions.
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
authors.forename: Bingyuan
authors.initials: B
authors.lastname: Wang
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
authors.forename: Wenbo
authors.initials: W
authors.lastname: Wan
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
authors.forename: Yihan
authors.initials: Y
authors.lastname: Wang
authors.affiliation: Cancer Institute and Hospital, Tianjin Medical University, Tianjin, 300060, China.
authors.forename: Wenjuan
authors.initials: W
authors.lastname: Ma
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
authors.forename: Limin
authors.initials: L
authors.lastname: Zhang
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
authors.forename: Jiao
authors.initials: J
authors.lastname: Li
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China.
authors.forename: Zhongxing
authors.initials: Z
authors.lastname: Zhou
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China. huijuanzhao@tju.edu.cn.|Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin, 300072, China. huijuanzhao@tju.edu.cn.
authors.forename: Huijuan
authors.initials: H
authors.lastname: Zhao
authors.affiliation: College of Precision Instruments and Optoelectronics Engineering, Tianjin University, Tianjin, 300072, China. gaofeng@tju.edu.cn.|Tianjin Key Laboratory of Biomedical Detecting Techniques and Instruments, Tianjin, 300072, China. gaofeng@tju.edu.cn.
authors.forename: Feng
authors.initials: F
authors.lastname: Gao
mesh_terms: D000465:Algorithms; D001940:Breast / Q000000981:diagnostic imaging*; D005260:Female; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D019047:Phantoms, Imaging; D041622:Tomography, Optical / Q000379:methods*
keywords: Diffuse optical tomography; Inverse problem; Non-negative; Sparsity regularization