An investigation on computed tomography image reconstruction with compressed sensing by l₁ norm prior image constraints

This paper aims to investigate the problem of low-dose computed tomography (CT) reconstruction with prior image constraints using the compressed sensing (CS) theorem. The CS theorem states that images can be reconstructed from under-sampled data in an adequate or transfer domain without introducing noticeable artifacts by solving a convex optimization problem if the source signals are sparse. To describe the sparsity, a model of piecewise constant source distribution has recently been assumed for image reconstruction by minimizing the total variance (TV) of the image density distribution in the Fourier domain. However, the assumption may not hold for complicated image structures. It has been observed that a prior image from the same subject or anatomy can provide excellent information to the image to be reconstructed. Based on this observation, this study investigates the problem of image reconstruction from under-sampled data by minimizing the difference between the prior image and the concerned image to be estimated with data constraints in the Fourier domain. Compared to the TV criterion, this presented method doesn't require the piecewise constant assumption where the similarity between the two images specifies a new priori model for a new cost function. The presented method was tested by computer simulations using the Shepp-Logan phantom. In noise-free case, only 64 projections around the phantom are needed to produce an accurate reconstruction. The reconstruction remained excellent until the number of projections was reduced to 22 when a high similarity exists between the prior and concerned images while the well-known filtered backprojection reconstruction failed. In cases with noise variance at 1% level, the signal-to-noise of the reconstruction by presented CS-based approach dropped rapidly when the number of projections decreased from 64 to 22. This investigation reveals the high sensitivity of the CS-based approach for low-dose CT image reconstruction. Modification of the cost function to consider data statistics is needed.