Nicolas Normand

Conjugate gradient Mojette reconstruction

Iterative methods are now recognized as powerful tools to solve inverse problems such as tomographic reconstruction. In this paper, the main goal is to present a new reconstruction algorithm made from two components. An iterative algorithm, namely the Conjugate Gradient (CG) method, is used to solve the tomographic problem in the least square (LS) sense for our specific discrete Mojette geometry. The results are compared (with the same geometry) to the corresponding Mojette Filtered Back Projection (FBP) method. In the fist part of the paper, we recall the discrete geometry used to define the projection M and backprojection M* operators. In the second part, the CG algorithm is presented within the context of the Mojette geometry. Noise is then added onto these Mojette projections with respect to the sampling and reconstructions are performed. Finally the Toeplitz block Toeplitz (TBT) character of M*M is demonstrated.

La transformée Mojette: une représentation redondante pour l'image

Resume Nous definissons une transformee dimage qui fournit un ensemble redondant dinformation. Cette transformee et sa transformee inverse sont construites a partir delements structurants a deux pixels. Les ordres de complexite associes sont comparables a ceux de la transformee de Fourier rapide.

Software tools dedicated for an automatic analysis of the CT scanner quality control images

This paper deals with the CT scanner images quality control, which is an important part of the quality control process of the CT scanner, which consists of making measurement in images of dedicated phantoms. Standard methods consist of scan explorations of phantoms that contain different specific patterns1, 2. These methods rely on manual measurements with graphics tools in corresponding images (density, position, length...) or automatic measurements developed in softwares3, 4 that use some masks to determine the region of interest (ROI). The problem of these masks is that they may produce wrong results in case of misalignment of the phantom. We propose a new method that consists, firstly of developing software tools that are capable of performing an automated analysis of CT images of three standard phantoms, LAP5 , GEMS6 and CATPHAN6007, in terms of slice thickness, spatial resolution, low and high level contrast, noise and uniformity. The method we have developed is completely automatic because it uses some protocols and special treatments in the images to automatically detect the position and the size of the ROI. Secondly, to test the performances of our software tools, we develop two digital phantoms which reproduce the exact geometry and composition of the physical phantoms, i.e. some perfect CT images of the real phantoms, and a complete set of distorted digital phantoms which represent the perfect phantom distorted by noise and blur calibrated functions to test the performances of our automated analysis software.

Joint source–channel coding: Secured and progressive transmission of compressed medical images on the Internet

The joint source-channel coding system proposed in this paper has two aims: lossless compression with a progressive mode and the integrity of medical data, which takes into account the priorities of the image and the properties of a network with no guaranteed quality of service. In this context, the use of scalable coding, locally adapted resolution (LAR) and a discrete and exact Radon transform, known as the Mojette transform, meets this twofold requirement. In this paper, details of this joint coding implementation are provided as well as a performance evaluation with respect to the reference CALIC coding and to unequal error protection using Reed-Solomon codes.

Secured and progressive transmission of compressed images on the Internet: application to telemedicine

Within the framework of telemedicine, the amount of images leads first to use efficient lossless compression methods for the aim of storing information. Furthermore, multiresolution scheme including Region of Interest (ROI) processing is an important feature for a remote access to medical images. What is more, the securization of sensitive data (e.g. metadata from DICOM images) constitutes one more expected functionality: indeed the lost of IP packets could have tragic effects on a given diagnosis. For this purpose, we present in this paper an original scalable image compression technique (LAR method) used in association with a channel coding method based on the Mojette Transform, so that a hierarchical priority encoding system is elaborated. This system provides a solution for secured transmission of medical images through low-bandwidth networks such as the Internet.

Scalable multiple descriptions on packets networks via the n-dimensional Mojette transform

The Mojette transform is a discrete projector generating bins from ixels (information elements) values. The initial bitstream is first rearranged into a 2D or n-dimensional box of ixels. Each bin value (belonging to a (n-1)-dimensional projection) is computed as the XOR addition of ixels belonging to a discrete line which fix the projection direction. The major advantage of this transform is the linear complexity (both in the number of ixels and the number of projections) for encoding and decoding. Each packet contains a projection, and additional projections can be computed without slowing the network flow. The size of this n-dimensional buffer is tuned according to the real- time constraints and to the desired packet size.

Automatic quality control of digitally reconstructed radiograph computation and comparison with standard methods

Conformal radiotherapy helps to deliver an accurate and effective cancer treatment by exactly targeting the tumor. In this purpose, softwares of the treatment planning system (TPS) compute every geometric parameters of the treatment. It is essential to control the quality of them because the TPS performances are directly connected with the precision on the treated region. The standard method to control them is to use physical test objects (PTOs).1, 2 The use of PTOs introduces uncertainties in the quality assessment because of the CT scan. Another method to assess the quality of these softwares is to use digital test objects (DTOs).3-5 DTOs are exactly known in a continuous and a discrete way. Thus the assessment of the TPS quality can be more accurate and faster. The fact that the DTO characteristics are well known allows to calculate a theoretical result. The comparison of the TPS and this theoretical results leads to a quantitative assessment of the TPS softwares quality. This work presents the control of major quality criteria of digitally reconstructed radiograph (DRR) computation: ray divergence, ray incidence and spatial resolution. Fully automated methods to control these points have been developed. The same criteria have been tested with PTO and the quality assessments by the two methods have been compared. The DTO methods appeared to be much more accurate because computable.

Noise behavior of spline Mojette FBP reconstruction

The goal of this paper is to characterize the noise properties of a spline Filtered BackProjection (denoted as FBP) reconstruction scheme. More specifically, the paper focuses on angular and radial sampling of projection data and on assumed local properties of the function to be reconstructed. This new method is visually and quantitatively compared to standard sampling used for FBP scheme. In the second section, we recall the sampling geometry adapted to the discrete geometry of the reconstructed image. Properties of the discrete zero order Spline Ramp filter for classic angles and discrete angles generated from Farey’s series reconstruction are used to generate their equivalent representations for first order Spline filters. Digital phantoms are used to assess the results and the correctness of the linearity and shift-invariantness assumption for the discrete reconstructions. The filter gain has been studied in the Mojette case since the number of projections can be very different from one angle to another. In the third section, we describe the Spline filter implementation and the continuous/discrete correspondence. In section 4, Poisson noise is added to noise-free onto the projections. The reconstructions between classic angle distribution and Mojette acquisition geometry are compared. Even if the number of bins per projections is fixed for classic FBP while it varies for the Mojette geometry (leading to very different noise behavior per bin) the results of both algorithms are very close. The discussion allows for a general comparison between classic FBP reconstruction and Mojette FBP. The very encouraging results obtained for the Mojette case conclude for the developments of future acquisition devices modeled with the Mojette geometry.

Systolic preprocessor for online morphologic operations

Mathematical morphology is a powerful and widespread tool for image analysis and coding. But for large analysis neighborhoods, it becomes rapidly time consuming on general purpose machines. Many works have been done to decrease the overall complexity by splitting heavy computation tasks into several more efficient ones. Even if significant speedup factors have been achieved using dedicated architectures, the major drawback is that the number of operations required is still dependent on the considered neighborhood size. This paper deals with a systolic network for real time morphological processing since it is able to perform erosions, dilations, openings, and closings during a unique image scan. It implements a new method called casual recursive erosion based on the decomposition of neighborhoods by both dilations and union sets. The resulting architecture presents a low complexity and offers a constant computation time. Reconfigurration of the application only consists in modifying a few array contents. System synthesis onto one FPGA yields very high processing rates.

Assessment of tomographic reconstruction performance using the Mojette transform

The Mojette transform is a discrete and exact Radon transform, based on the discrete geometry of the projection and reconstruction lattice. The specific sampling scheme of the Mojette transform results in theoretical exact image reconstruction. In this paper, we compare the reconstructions obtained with the Mojette transform to the ones obtained with several usual projection/backprojection digitized Radon transform. These experiments validate and demonstrate the performance of the Mojette transform sampling over classical implementations based on continuous space.