Convolutional Neural Networks (CNNs) and Transformer-based self-attention models have become the standard for medical image segmentation. This paper demonstrates that convolution and self-attention, while widely used, are not the only effective methods for segmentation. Breaking with convention, we present a Convolution and self-Attention-free Mamba-based seman-tic Segmentation Network named CAMS-Net. Specifically, we design Mamba-based Channel Aggregator and Spatial Aggregator, which are applied independently in each encoder-decoder stage. The Channel Aggregator extracts information across different channels, and the Spatial Ag-gregator learns features across different spatial locations. We also propose a Linearly Interconnected Factorized Mamba (LIFM) block to reduce the computational complexity of a Mamba block and to enhance its decision function by introducing a non-linearity between two factor-ized Mamba blocks. Our model outperforms the existing state-of-the-art CNN, self-attention, and Mamba-based methods on CMR and M&Ms-2 Cardiac segmentation datasets, showing how this innovative, convolution, and self-attention-free method can inspire further research beyond CNN and Transformer paradigms, achieving linear complexity and reducing the number of parameters. Source code and pre-trained models are available at: https://github.com/kabbas570/CAMS-Net.

Cardiac image segmentation is essential for automated cardiac function assessment and monitoring of changes in cardiac structures over time. Inspired by coarse-to-fine approaches in image analysis, we propose a novel multitask compositional segmentation approach that can simultaneously localize the heart in a cardiac image and perform part-based segmentation of different regions of interest. We demonstrate that this compositional approach achieves better results than direct segmentation of the anatomies. Further, we propose a novel Cross-Modal Feature Integration (CMFI) module to leverage the meta-data related to cardiac imaging collected during image acquisition. We perform experiments on two different modalities, MRI and ultrasound, using public datasets, Multi-Disease, Multi-View, and Multi-Centre (M &Ms-2) and Multi-structure Ultrasound Segmentation (CAMUS) data, to showcase the efficiency of the proposed compositional segmentation method and Cross-Modal Feature Integration module incorporating metadata within the proposed compositional segmentation network. The source code is available: https://github.com/kabbas570/CompSeg-MetaData.

We introduce a novel mathematical formulation for the training of feed-forward neural networks with (potentially non-smooth) proximal maps as activation functions. This formulation is based on Bregman distances and a key advantage is that its partial derivatives with respect to the network’s parameters do not require the computation of derivatives of the network's activation functions. Instead of estimating the parameters with a combination of first-order optimisation method and back-propagation (as is the state-of-the-art), we propose the use of non-smooth first-order optimisation methods that exploit the specific structure of the novel formulation. We present several numerical results that demonstrate that these training approaches can be equally well or even better suited for the training of neural network-based classifiers and (denoising) autoencoders with sparse coding compared to more conventional training frameworks.

This work investigates the application of deep learning to timbre transfer. The adopted approach combines Variational Autoencoders with Generative Adversarial Networks to construct meaningful representations of the source audio and produce realistic generations of the target audio and is applied to the Flickr 8k Audio dataset for transferring the vocal timbre between speakers and the URMP dataset for transferring the musical timbre between instruments. Variations of the adopted approach were trained, and performance was compared using the metrics SSIM (Structural Similarity Index) and FAD (Frechét Audio Distance). It was found that a many-to-many approach supersedes a one-to-one approach in terms of reconstructive capabilities, while one-to-one showed better results in terms of adversarial translation. The adoption of a basic over a bottleneck residual block design is more suitable for enriching content information about a latent space, and the decision on whether cyclic loss takes on a variational autoencoder or vanilla auto encoder approach does not have a significant impact on reconstructive and adversarial translation aspects of the model.

We propose an extension of a special form of gradient descent---in the literature known as linearized Bregman iteration---to a larger class of nonconvex functions. We replace the classical (squared) two norm metric in the gradient descent setting with a generalized Bregman distance, based on a proper, convex, and lower semicontinuous function. The algorithm's global convergence is proven for functions that satisfy the Kurdyka--Łojasiewicz property. Examples illustrate that features of different scale are being introduced throughout the iteration, transitioning from coarse to fine. This coarse-to-fine approach with respect to scale allows us to recover solutions of nonconvex optimization problems that are superior to those obtained with conventional gradient descent, or even projected and proximal gradient descent. The effectiveness of the linearized Bregman iteration in combination with early stopping is illustrated for the applications of parallel magnetic resonance imaging, blind deconvolution, as well as image classification with neural networks.

The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long acquisition times can limit its use. In this work, we consider the problem of learning a sparse sampling pattern that can be used to optimally balance acquisition time versus quality of the reconstructed image. We use a supervised learning approach, making the assumption that our training data is representative enough of new data acquisitions. We demonstrate that this is indeed the case, even if the training data consists of just 7 training pairs of measurements and ground-truth images; with a training set of brain images of size 192 by 192, for instance, one of the learned patterns samples only 35% of k-space, however results in reconstructions with mean SSIM 0.914 on a test set of similar images. The proposed framework is general enough to learn arbitrary sampling patterns, including common patterns such as Cartesian, spiral and radial sampling.

This paper deals with the problem of reconstructing a depth map from a sequence of differently focused images, also known as depth from focus (DFF) or shape from focus. We propose to state the DFF problem as a variational problem, including a smooth but nonconvex data fidelity term and a convex nonsmooth regularization, which makes the method robust to noise and leads to more realistic depth maps. In addition, we propose to solve the nonconvex minimization problem with a linearized alternating directions method of multipliers, allowing to minimize the energy very efficiently. A numerical comparison to classical methods on simulated as well as on real data is presented.