title: Total variation minimization filter for DBT imaging.
abstract: OBJECTIVE
  Compressed sensing (CS) is a new approach in medical imaging which allows a sparse image to be reconstructed from undersampled data. Total variation (TV) based minimization algorithms are the one CS technique that has achieved great success due to its virtue of preserving edges while reducing image noise. The purpose of this work is to implement and evaluate the performance of a TV minimization filter able to increase the signal difference to noise ratio (SDNR) of digital breast tomosynthesis (DBT) images.
  
  
  METHODS
  Assuming a Poisson noise model, the authors present a practical methodology, based on Rudin, Osher, and Fatemi model, which directly applies a TV minimization filter to real phantom and clinical DBT images. Different moments of filter application (before and after image reconstruction) and the suitable Lagrange multiplier (λ) to be used in filter equation are studied. Also, the relationship between background standard deviation (σB) of unfiltered images and optimal λ values is determined, in order to maximize the SDNR. Qualitative and quantitative analyses are conducted between unfiltered and filtered images and between the different moments of filter application. The proposed methodology is also tested with one clinical DBT data set.
  
  
  RESULTS
  Using phantom data, when the filter is applied to the projections, the authors observed a decrease of 31.34% in TV and an increase of 5.29% and 5.44% in SDNR and full width at half maximum (FWHM), respectively. When applied after reconstruction, a decrease of 35.48% and 2.59% was achieved for TV and FWHM, respectively, and an increase of 8.32% for SDNR. For each moment of filter application, the optimal λ value found through a comprehensive study was λ = 85 and λ = 60 when the filter is applied before and after reconstruction, respectively. The best fit found for the relationship between σB and the corresponding λ values that allowed the highest filtered SDNR was the logarithmic adjustment. The difference between the λ values obtained by the first approach and the logarithmic adjustment ranges from 0.11% (filter applied before reconstruction) to 2.54% (filter applied after reconstruction). On the other hand, a decrease of 37.63% and 2.42% in TV and FWHM, respectively, and an increase of 24.39% in SDNR were obtained when the filter is applied to clinical data. This great minimization is present through a visual inspection of unfiltered and filtered clinical images, where areas with higher noise level become smoother while preserving edges and details of the structures.
  
  
  CONCLUSIONS
  An optimized digital filter for TV minimization in DBT imaging has been presented. The reliability of a logarithmic relation found between σB and λ values was confirmed and can be used in future work. Both quantitative and qualitative analyses performed in a clinical DBT image confirmed the relevance of this approach in improving image quality in DBT imaging. The results obtained are very encouraging about increasing SDNR in a short time and preserving the principal variations in image, the structures' boundary.
authors.affiliation: Universidade de Lisboa, Faculdade de Ciências, Instituto de Biofísica e Engenharia Biomédica, Campo Grande, Lisboa 1749-016, Portugal.
authors.forename: Ana M
authors.initials: AM
authors.lastname: Mota
authors.affiliation: Universidade de Lisboa, Faculdade de Ciências, Instituto de Biofísica e Engenharia Biomédica, Campo Grande, Lisboa 1749-016, Portugal.
authors.forename: Nuno
authors.initials: N
authors.lastname: Matela
authors.affiliation: Universidade de Lisboa, Faculdade de Ciências, Instituto de Biofísica e Engenharia Biomédica, Campo Grande, Lisboa 1749-016, Portugal.
authors.forename: Nuno
authors.initials: N
authors.lastname: Oliveira
authors.affiliation: Universidade de Lisboa, Faculdade de Ciências, Instituto de Biofísica e Engenharia Biomédica, Campo Grande, Lisboa 1749-016, Portugal.
authors.forename: Pedro
authors.initials: P
authors.lastname: Almeida
mesh_terms: D000465:Algorithms; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008327:Mammography / Q000379:methods*; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D059629:Signal-To-Noise Ratio