Encoding-decoding (ED) CNNs have demonstrated state-of-the-art performance for noise reduction over the past years. This has triggered the pursuit of better understanding the inner workings of such architectures, which has led to the theory of deep convolutional framelets (TDCF), revealing important links between signal processing and CNNs. Specifically, the TDCF demonstrates that ReLU CNNs induce low-rankness, since these models often do not satisfy the necessary redundancy to achieve perfect reconstruction (PR). In contrast, this paper explores CNNs that do meet the PR conditions. We demonstrate that in these type of CNNs soft shrinkage and PR can be assumed. Furthermore, based on our explorations we propose the learned wavelet-frame shrinkage network, or LWFSN and its residual counterpart, the rLWFSN. The ED path of the (r)LWFSN complies with the PR conditions, while the shrinkage stage is based on the linear expansion of thresholds proposed Blu and Luisier. In addition, the LWFSN has only a fraction of the training parameters (<1%) of conventional CNNs, very small inference times, low memory footprint, while still achieving performance close to state-of-the-art alternatives, such as the tight frame (TF) U-Net and FBPConvNet, in low-dose CT denoising.

In biopsies, drainages, vertebroplasty, and other needle-based procedures, insight on the 3D position of a needle is crucial for correct navigation by the clinician. In this paper, we present a method for the reconstruction of surgical needles using multi-view X-ray imaging with a small motion of the C-arm. It is required that the extent of the motion is limited (<; 30 degrees) to allow use of this method during an intervention. This small motion provides sufficient multi-view information, which is used in combination with a needle model for the 3D reconstruction of the needle. To this end, we describe a system comprising the steps of (a) needle detection in a novel, RANSAC-based framework, (b) tracking of needles in subsequent views using geometric constraints and (c) needle reconstruction. Results are presented in comparison to a volume reconstruction using a full rotation of the C-arm (≈207 degrees), showing good accuracy of the proposed method.

In this paper, we build on the RANSAC method to detect multiple instances of objects in an image, where the objects are modeled as curvilinear segments with distinct endpoints. Our approach differs from previously presented work in that it incorporates soft constraints, based on a dense image representation, that guide the estimation process in every step. This enables (1) better correspondence with image content, (2) explicit endpoint detection and (3) a reduction in the number of iterations required for accurate estimation. In the case of curvilinear objects examined in this paper, these constraints are formulated as binary image labels, where the estimation proved to be robust to mislabeling, e.g. in case of intersections. Results for both synthetic and real data from medical X-ray images show the improvement from incorporating soft image-based constraints.