Prior image constrained compressed sensing: implementation and performance evaluation

Prior image constrained compressed sensing (PICCS) is an image reconstruction framework which incorporates an often available prior image into the compressed sensing objective function. The images are reconstructed using an optimization procedure. In this paper, several alternative unconstrained minimization methods are used to implement PICCS. The purpose is to study and compare the performance of each implementation, as well as to evaluate the performance of the PICCS objective function with respect to image quality.

Six different minimization methods are investigated with respect to convergence speed and reconstruction accuracy. These minimization methods include the steepest descent (SD) method and the conjugate gradient (CG) method. These algorithms require a line search to be performed. Thus, for each minimization algorithm, two line searching algorithms are evaluated: a backtracking (BT) line search and a fast Newton-Raphson (NR) line search. The relative root mean square error is used to evaluate the reconstruction accuracy. The algorithm that offers the best convergence speed is used to study the performance of PICCS with respect to the prior image parameter α and the data consistency parameter λ. PICCS is studied in terms of reconstruction accuracy, low-contrast spatial resolution, and noise characteristics. A numerical phantom was simulated and an animal model was scanned using a multirow detector computed tomography (CT) scanner to yield the projection datasets used in this study.

For λ within a broad range, the CG method with Fletcher-Reeves formula and NR line search offers the fastest convergence for an equal level of reconstruction accuracy. Using this minimization method, the reconstruction accuracy of PICCS was studied with respect to variations in α and λ. When the number of view angles is varied between 107, 80, 64, 40, 20, and 16, the relative root mean square error reaches a minimum value for α ≈ 0.5. For values of α near the optimal value, the spatial resolution of the reconstructed image remains relatively constant and the noise texture is very similar to that of the prior image, which was reconstructed using the filtered backprojection (FBP) algorithm.

Regarding the performance of the minimization methods, the nonlinear CG method with NR line search yields the best convergence speed. Regarding the performance of the PICCS image reconstruction, three main conclusions can be reached. (1) The performance of PICCS is optimal when the weighting parameter of the prior image parameter is selected to be near α = 0.5. (2) The spatial resolution measured for static objects in images reconstructed using PICCS from undersampled datasets is not degraded with respect to the fully-sampled reconstruction for α near its optimal value. (3) The noise texture of PICCS reconstructions is similar to that of the prior image, which was reconstructed using the conventional FBP method.