Compressed sensing in digital tomosynthesis reconstruction

In this work we study a model for the breast image reconstruction in Digital Tomosynthesis, that is a non-invasive and non-destructive method for the three-dimensional visualization of the inner structures of an object, in which the data acquisition includes measuring a limited number of low-dose two-dimensional projections of an object by moving a detector and an X-ray tube around the object within a limited angular range. The problem of reconstructing 3D images from the projections provided in the Digital Tomosynthesis is an ill-posed inverse problem, that leads to a minimization problem with an object function that contains a data fitting term and a regularization term. The contribution of this thesis is to use the techniques of the compressed sensing, in particular replacing the standard least squares problem of data fitting with the problem of minimizing the 1-norm of the residuals, and using as regularization term the Total Variation (TV). We tested two different algorithms: a new alternating minimization algorithm (ADM), and a version of the more standard scaled projected gradient algorithm (SGP) that involves the 1-norm. We perform some experiments and analyse the performance of the two methods comparing relative errors, iterations number, times and the qualities of the reconstructed images. In conclusion we noticed that the use of the 1-norm and the Total Variation are valid tools in the formulation of the minimization problem for the image reconstruction resulting from Digital Tomosynthesis and the new algorithm ADM has reached a relative error comparable to a version of the classic algorithm SGP and proved best in speed and in the early appearance of the structures representing the masses.

QUANTITATIVE THREE DIMENSIONAL ELASTICITY IMAGING

Neoplastic tissue is typically highly vascularized, contains abnormal concentrations of extracellular proteins (e.g. collagen, proteoglycans) and has a high interstitial fluid pres- sure compared to most normal tissues. These changes result in an overall stiffening typical of most solid tumors. Elasticity Imaging (EI) is a technique which uses imaging systems to measure relative tissue deformation and thus noninvasively infer its mechanical stiffness. Stiffness is recovered from measured deformation by using an appropriate mathematical model and solving an inverse problem. The integration of EI with existing imaging modal- ities can improve their diagnostic and research capabilities. The aim of this work is to develop and evaluate techniques to image and quantify the mechanical properties of soft tissues in three dimensions (3D). To that end, this thesis presents and validates a method by which three dimensional ultrasound images can be used to image and quantify the shear modulus distribution of tissue mimicking phantoms. This work is presented to motivate and justify the use of this elasticity imaging technique in a clinical breast cancer screening study. The imaging methodologies discussed are intended to improve the specificity of mammography practices in general. During the development of these techniques, several issues concerning the accuracy and uniqueness of the result were elucidated. Two new algorithms for 3D EI are designed and characterized in this thesis. The first provides three dimensional motion estimates from ultrasound images of the deforming ma- terial. The novel features include finite element interpolation of the displacement field, inclusion of prior information and the ability to enforce physical constraints. The roles of regularization, mesh resolution and an incompressibility constraint on the accuracy of the measured deformation is quantified. The estimated signal to noise ratio of the measured displacement fields are approximately 1800, 21 and 41 for the axial, lateral and eleva- tional components, respectively. The second algorithm recovers the shear elastic modulus distribution of the deforming material by efficiently solving the three dimensional inverse problem as an optimization problem. This method utilizes finite element interpolations, the adjoint method to evaluate the gradient and a quasi-Newton BFGS method for optimiza- tion. Its novel features include the use of the adjoint method and TVD regularization with piece-wise constant interpolation. A source of non-uniqueness in this inverse problem is identified theoretically, demonstrated computationally, explained physically and overcome practically. Both algorithms were test on ultrasound data of independently characterized tissue mimicking phantoms. The recovered elastic modulus was in all cases within 35% of the reference elastic contrast. Finally, the preliminary application of these techniques to tomosynthesis images showed the feasiblity of imaging an elastic inclusion.

Comparative performance of multiview stereoscopic and mammographic display modalities for breast lesion detection.

PURPOSE: Mammography is known to be one of the most difficult radiographic exams to interpret. Mammography has important limitations, including the superposition of normal tissue that can obscure a mass, chance alignment of normal tissue to mimic a true lesion and the inability to derive volumetric information. It has been shown that stereomammography can overcome these deficiencies by showing that layers of normal tissue lay at different depths. If standard stereomammography (i.e., a single stereoscopic pair consisting of two projection images) can significantly improve lesion detection, how will multiview stereoscopy (MVS), where many projection images are used, compare to mammography? The aim of this study was to assess the relative performance of MVS compared to mammography for breast mass detection. METHODS: The MVS image sets consisted of the 25 raw projection images acquired over an arc of approximately 45 degrees using a Siemens prototype breast tomosynthesis system. The mammograms were acquired using a commercial Siemens FFDM system. The raw data were taken from both of these systems for 27 cases and realistic simulated mass lesions were added to duplicates of the 27 images at the same local contrast. The images with lesions (27 mammography and 27 MVS) and the images without lesions (27 mammography and 27 MVS) were then postprocessed to provide comparable and representative image appearance across the two modalities. All 108 image sets were shown to five full-time breast imaging radiologists in random order on a state-of-the-art stereoscopic display. The observers were asked to give a confidence rating for each image (0 for lesion definitely not present, 100 for lesion definitely present). The ratings were then compiled and processed using ROC and variance analysis. RESULTS: The mean AUC for the five observers was 0.614 +/- 0.055 for mammography and 0.778 +/- 0.052 for multiview stereoscopy. The difference of 0.164 +/- 0.065 was statistically significant with a p-value of 0.0148. CONCLUSIONS: The differences in the AUCs and the p-value suggest that multiview stereoscopy has a statistically significant advantage over mammography in the detection of simulated breast masses. This highlights the dominance of anatomical noise compared to quantum noise for breast mass detection. It also shows that significant lesion detection can be achieved with MVS without any of the artifacts associated with tomosynthesis.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Mammography equipment

Mammography is one of the most technically demanding examinations in radiology, and it requires X-ray technology designed specifi cally for the task. The pathology to be imaged ranges from small (20–100 μm) high density microcalcifications to ill-defi ned low contrast masses. These must be imaged against a background of mixed densities. This makes demonstrating pathology challenging. Because of its use in asymptomatic screening, mammography must also employ as low a radiation dose as possible.