Quantitative Ultrasound (QUS) is a non-invasive imaging modality that characterizes tissues numerically. A well-known QUS parameter is the attenuation coefficient slope (ACS). A previous work proposed a regularized spectral log difference method (RSLD) to estimate the ACS, yet the ACS and the backscatter component were computed as independent parameters using a single channel total variation with no joint prior exploited. This work proposes a joint reconstruction method named the Total Nuclear Variation SLD (TNV-SLD). It couples geometrical information of the ACS and the backscatter component to enhance the quality of the images, measured by the mean percentage error (MPE) and contrast-to-noise ratio (CNR). Metrics are compared to the RSLD with data from a simulated and a physical phantom. Initial results show that TNV-SLD can provide comparable CNR values than RSLD but with lower MPE values. In the simulation, RSLD achieved a MPE of 25.4% (inclusion) and 8.1% (background), while TNV-SLD obtained MPE of 15.9% (inclusion) and 2.8% (background). In the real phantom, RSLD achieved a MPE of 37.7% (inclusion) and 1.9% (background), while TNV-SLD obtained MPE of 22.5% (inclusion) and 1.8% (background). Furthermore, TNV-SLD was more robust in terms of the regularization parameter µ, maintaining a more s table MPE and a higher CNR than RSLD for a broader range of µ values, thus surpassing the risk of over-regularizing the images.