Nourelhouda Groun

Data-driven modal decomposition techniques are methods with sound mathematical foundation, used to analyze and extract useful information from complex datasets. These techniques rely heavily on numerical linear algebra concepts. Consider the singular value decomposition (SVD), which is considered the most important matrix factorization of the computational era. This method is representative of most of the data-driven methods. Hence, this basis will allow us to interpret most of these modal decomposition techniques as matrix factorization approaches. Among the plethora of modal decomposition techniques, in this contribution, we focus on one of the most well-known data-driven techniques, the dynamic mode decomposition (DMD). This technique was originally introduced in the field of fluid mechanics, but extended its application to cover plentiful other fields (biology, healthcare, sports ...). Following its great success in these different fields, many researchers have worked on developing extensions of this technique, which can be more robust, more accurate and cover a wider range of applications. We introduce one of these extensions, named the higher order dynamic mode decomposition (HODMD), which is widely used in fluid dynamics applications. The HODMD method excels at identifying and extracting dominant patterns representing the complex dynamics of fluid flows. In this contribution, we shift the domain of applications of the HODMD technique from fluid dynamics to the medical field. More specifically, we consider the analysis of data obtained from common use medical imaging techniques. The investigation of this technique on medical data has led not only to the demonstration of the robustness of the HODMD applications, but also to the discovery of several, new applications. First, the HODMD technique is used to analyze echocardiography video loops taken from mice in healthy conditions and mice afflicted with different cardiac diseases (diabetic cardiomyopathy, obesity, TAC hypertrophy or myocardial infarction). The outcome of this first application proves, once again, the efficiency of the HODMD algorithm in pattern identification and feature extraction, as the technique was able to capture and represent the dominant features related to the different cardiac conditions. Second, the HODMD algorithm is used for the analysis of sequences of Magnetic Resonance Imaging (MRI). In this application the HODMD is used first as a reduced order model (ROM) to generate new, extended databases. Furthermore, the HODMD is combined with a novel interpolation technique with the aim of recovering missing information and the reconstruction of corrupted images. RESUMEN Las técnicas de descomposición modal basadas en datos son métodos con una base matemática sólida, que se utilizan para analizar y extraer información útil de conjuntos de datos complejos. Estas técnicas se basan en gran medida en conceptos de álgebra lineal numérica. Considere la Singular Value Decomposition (SVD), que se considera la factorización de matrices más importante de la era computacional. Este método es representativo de la mayoría de los métodos basados en datos. Por lo tanto, esta base nos permitirá interpretar la mayoría de estas técnicas de descomposición modal como enfoques de factorización de matrices. Sin embargo, entre la plétora de técnicas de descomposición modal, en esta contribución, nos centramos en una de las técnicas basadas en datos más conocidas, la Dynamic Mode Decomposition (DMD). Esta técnica se introdujo originalmente en el campo de la mecánica de fluidos, pero extendió su aplicación a muchos otros campos (biología, salud, deportes...). Tras su gran éxito en estos diferentes campos, muchos investigadores han trabajado en el desarrollo de extensiones de esta técnica, que pueden ser más robustas, más precisas y cubrir una gama más amplia de aplicaciones. Presentamos una de estas extensiones, Higher Order Dynamic Mode Decomposition (HODMD). Esta técnica, es ampliamente utilizada en aplicaciones de dinámica de fluidos. El método HODMD sobresale en la identificación y extracción de patrones dominantes que representan la dinámica compleja de los flujos de fluidos. En esta contribución, cambiamos el dominio de aplicaciones de la técnica HODMD de la dinámica de fluidos al campo médico. Más específicamente, consideramos el análisis de datos obtenidos de técnicas de imágenes médicas de uso común. La investigación de esta técnica en datos médicos ha llevado no solo a la demostración de la robustez de las aplicaciones HODMD, sino también al descubrimiento de varias aplicaciones nuevas. Primero, la técnica HODMD se usa para analizar bucles de video de ecocardiografía tomados de ratones en condiciones saludables y ratones afectados por diferentes enfermedades cardíacas (miocardiopatía diabética, obesidad, hipertrofia TAC o infarto de miocardio). El resultado de esta primera aplicación demuestra, una vez más, la eficiencia del algoritmo HODMD en la identificación de patrones y extracción de características, ya que la técnica fue capaz de capturar y representar las características dominantes relacionadas con las diferentes condiciones cardíacas. Segundo, el algoritmo HODMD se utiliza para el análisis de secuencias de Imágenes por Resonancia Magnética (MRI). En esta aplicación, el HODMD se usa primero como un Reduced Order Model (ROM) para generar nuevas bases de datos ampliadas. Además, el HODMD se combina con una novedosa técnica de interpolación con el objetivo de recuperar información faltante y reconstruir imágenes corruptas....

In the realm of cardiovascular medicine, medical imaging plays a crucial role in accurately classifying cardiac diseases and making precise diagnoses. However, the field faces significant challenges when integrating data science techniques, as a significant volume of images is required for these techniques. As a consequence, it is necessary to investigate different avenues to overcome this challenge. In this contribution, we offer an innovative tool to conquer this limitation. In particular, we delve into the application of a well recognized method known as the EigenFaces approach to classify cardiac diseases. This approach was originally motivated for efficiently representing pictures of faces using principal component analysis, which provides a set of eigenvectors (aka eigenfaces), explaining the variation between face images. As this approach proven to be efficient for face recognition, it motivated us to explore its efficiency on more complicated data bases. In particular, we integrate this approach, with convolutional neural networks (CNNs) to classify echocardiography images taken from mice in five distinct cardiac conditions (healthy, diabetic cardiomyopathy, myocardial infarction, obesity and TAC hypertension). Performing a preprocessing step inspired from the eigenfaces approach on the echocardiography datasets, yields sets of pod modes, which we will call eigenhearts. To demonstrate the proposed approach, we compare two testcases: (i) supplying the CNN with the original images directly, (ii) supplying the CNN with images projected into the obtained pod modes. The results show a substantial and noteworthy enhancement when employing SVD for pre-processing, with classification accuracy increasing by approximately 50%.

In this work, a data-driven, modal decomposition method, the higher order dynamic mode decomposition (HODMD), is combined with a convolutional neural network (CNN) in order to improve the classification accuracy of several cardiac diseases using echocardiography images. The HODMD algorithm is used first as feature extraction technique for the echocardiography datasets, taken from both healthy mice and mice afflicted by different cardiac diseases (Diabetic Cardiomyopathy, Obesity, TAC Hypertrophy and Myocardial Infarction). A total number of 130 echocardiography datasets are used in this work. The dominant features related to each cardiac disease were identified and represented by the HODMD algorithm as a set of DMD modes, which then are used as the input to the CNN. In a way, the database dimension was augmented, hence HODMD has been used, for the first time to the authors knowledge, for data augmentation in the machine learning framework. Six sets of the original echocardiography databases were hold out to be used as unseen data to test the performance of the CNN. In order to demonstrate the efficiency of the HODMD technique, two testcases are studied: the CNN is first trained using the original echocardiography images only, and second training the CNN using a combination of the original images and the DMD modes. The classification performance of the designed trained CNN shows that combining the original images with the DMD modes improves the results in all the testcases, as it improves the accuracy by up to 22%. These results show the great potential of using the HODMD algorithm as a data augmentation technique.

Heart diseases are the main international cause of human defunction. According to the WHO, nearly 18 million people decease each year because of heart diseases. Also considering the increase of medical data, much pressure is put on the health industry to develop systems for early and accurate heart disease recognition. In this work, an automatic cardiac pathology recognition system based on a novel deep learning framework is proposed, which analyses in real-time echocardiography video sequences. The system works in two stages. The first one transforms the data included in a database of echocardiography sequences into a machine-learning-compatible collection of annotated images which can be used in the training stage of any kind of machine learning-based framework, and more specifically with deep learning. This includes the use of the Higher Order Dynamic Mode Decomposition (HODMD) algorithm, for the first time to the authors' knowledge, for both data augmentation and feature extraction in the medical field. The second stage is focused on building and training a Vision Transformer (ViT), barely explored in the related literature. The ViT is adapted for an effective training from scratch, even with small datasets. The designed neural network analyses images from an echocardiography sequence to predict the heart state. The results obtained show the superiority of the proposed system and the efficacy of the HODMD algorithm, even outperforming pretrained Convolutional Neural Networks (CNNs), which are so far the method of choice in the literature.