Learning with noise and regularizers in multilayer neural networks

We study the effect of two types of noise, data noise and model noise, in an on-line gradient-descent learning scenario for general two-layer student network with an arbitrary number of hidden units. Training examples are randomly drawn input vectors labeled by a two-layer teacher network with an arbitrary number of hidden units. Data is then corrupted by Gaussian noise affecting either the output or the model itself. We examine the effect of both types of noise on the evolution of order parameters and the generalization error in various phases of the learning process.

Classification and contextual enhancement of remotely sensed data

The aims of the project were twofold: 1) To investigate classification procedures for remotely sensed digital data, in order to develop modifications to existing algorithms and propose novel classification procedures; and 2) To investigate and develop algorithms for contextual enhancement of classified imagery in order to increase classification accuracy. The following classifiers were examined: box, decision tree, minimum distance, maximum likelihood. In addition to these the following algorithms were developed during the course of the research: deviant distance, look up table and an automated decision tree classifier using expert systems technology. Clustering techniques for unsupervised classification were also investigated. Contextual enhancements investigated were: mode filters, small area replacement and Wharton's CONAN algorithm. Additionally methods for noise and edge based declassification and contextual reclassification, non-probabilitic relaxation and relaxation based on Markov chain theory were developed. The advantages of per-field classifiers and Geographical Information Systems were investigated. The conclusions presented suggest suitable combinations of classifier and contextual enhancement, given user accuracy requirements and time constraints. These were then tested for validity using a different data set. A brief examination of the utility of the recommended contextual algorithms for reducing the effects of data noise was also carried out.

New regularization method for EXAFS analysis: Application to uranium and plutonium sorption onto kaolinite

Die Röntgenabsorptionsspektroskopie (Extended X-ray absorption fine structure (EXAFS) spectroscopy) ist eine wichtige Methode zur Speziation von Schwermetallen in einem weiten Bereich von umweltrelevanten Systemen. Um Strukturparameter wie Koordinationszahl, Atomabstand und Debye-Waller Faktoren für die nächsten Nachbarn eines absorbierenden Atoms zu bestimmen, ist es für experimentelle EXAFS-Spektren üblich, unter Verwendung von Modellstrukturen einen „Least-Squares-Fit“ durchzuführen. Oft können verschiedene Modellstrukturen mit völlig unterschiedlicher chemischer Bedeutung die experimentellen EXAFS-Daten gleich gut beschreiben. Als gute Alternative zum konventionellen Kurven-Fit bietet sich das modifizierte Tikhonov-Regularisationsverfahren an. Ergänzend zur Tikhonov-Standardvariationsmethode enthält der in dieser Arbeit vorgestellte Algorithmus zwei weitere Schritte, nämlich die Anwendung des „Method of Separating Functionals“ und ein Iterationsverfahren mit Filtration im realen Raum. Um das modifizierte Tikhonov-Regularisationsverfahren zu testen und zu bestätigen wurden sowohl simulierte als auch experimentell gemessene EXAFS-Spektren einer kristallinen U(VI)-Verbindung mit bekannter Struktur, nämlich Soddyit (UO2)2SiO4 x 2H2O, untersucht. Die Leistungsfähigkeit dieser neuen Methode zur Auswertung von EXAFS-Spektren wird durch ihre Anwendung auf die Analyse von Proben mit unbekannter Struktur gezeigt, wie sie bei der Sorption von U(VI) bzw. von Pu(III)/Pu(IV) an Kaolinit auftreten. Ziel der Dissertation war es, die immer noch nicht voll ausgeschöpften Möglichkeiten des modifizierten Tikhonov-Regularisationsverfahrens für die Auswertung von EXAFS-Spektren aufzuzeigen. Die Ergebnisse lassen sich in zwei Kategorien einteilen. Die erste beinhaltet die Entwicklung des Tikhonov-Regularisationsverfahrens für die Analyse von EXAFS-Spektren von Mehrkomponentensystemen, insbesondere die Wahl bestimmter Regularisationsparameter und den Einfluss von Mehrfachstreuung, experimentell bedingtem Rauschen, etc. auf die Strukturparameter. Der zweite Teil beinhaltet die Speziation von sorbiertem U(VI) und Pu(III)/Pu(IV) an Kaolinit, basierend auf experimentellen EXAFS-Spektren, die mit Hilfe des modifizierten Tikhonov-Regularisationsverfahren ausgewertet und mit Hilfe konventioneller EXAFS-Analyse durch „Least-Squares-Fit“ bestätigt wurden.

An empirical evaluation of the Random Forests classifier models for variable selection in a large-scale lung cancer case-control study

Random Forests™ is reported to be one of the most accurate classification algorithms in complex data analysis. It shows excellent performance even when most predictors are noisy and the number of variables is much larger than the number of observations. In this thesis Random Forests was applied to a large-scale lung cancer case-control study. A novel way of automatically selecting prognostic factors was proposed. Also, synthetic positive control was used to validate Random Forests method. Throughout this study we showed that Random Forests can deal with large number of weak input variables without overfitting. It can account for non-additive interactions between these input variables. Random Forests can also be used for variable selection without being adversely affected by collinearities. ^ Random Forests can deal with the large-scale data sets without rigorous data preprocessing. It has robust variable importance ranking measure. Proposed is a novel variable selection method in context of Random Forests that uses the data noise level as the cut-off value to determine the subset of the important predictors. This new approach enhanced the ability of the Random Forests algorithm to automatically identify important predictors for complex data. The cut-off value can also be adjusted based on the results of the synthetic positive control experiments. ^ When the data set had high variables to observations ratio, Random Forests complemented the established logistic regression. This study suggested that Random Forests is recommended for such high dimensionality data. One can use Random Forests to select the important variables and then use logistic regression or Random Forests itself to estimate the effect size of the predictors and to classify new observations. ^ We also found that the mean decrease of accuracy is a more reliable variable ranking measurement than mean decrease of Gini. ^

An intelligent portable sensor system in diagnosing stress

Nowadays the stress is a frequent problem in the society. The level of stress could be important in order to recognise health problems later. Electrocardiogram technics allows to supervise the heart condition and the detection of anomalies about the patient. Sometimes the data collection systems by sensors placed on the patient restrict his mobility. Therefore the elimination of wires is a good solution for this trouble. Then the Bluetooth protocol is chosen as way for transmitting and receive data between stations. There are three ECG sensors placed on the right hand, the left hand and the right leg. It is possible to measure the heart signal with this technique. Besides there is an extra sensor in order to measure the temperature of the patient. Depending of the value of these parameters is possible to recognise stress levels. All sensors are connected to a special box with a microcontroller which treat every signal. This module has a Bluetooth part that transmitts wireless the new digital signal to the receiver. This one will be a dongle connected to the computer by Serial Port. A program in the computer has been implemented in order to receive the Bluetooth Data sent from the box and saving the data in a file for subsequent activities. El objetivo principal de este proyecto es el estudio de parámetros como la temperatura corporal y las señales de electrocardiograma para el diagnóstico del estrés. Existen varios estudios que relacionan estos parámetros y sus niveles con posibles casos de estrés y ansiedad. Para este fin usamos unos sensores colocados en el brazo derecho, brazo izquierdo y pierna izquierda. Esto forma el Eindhoven Triangle, que es conocido por dar una señal de electrocardiograma. A su vez también tendremos un sensor de temperatura colocado en un dedo de la mano para medir los grados a los que está el cuerpo en ese momento y así poder detectar ciertas anomalías. Estos sensores están conectados a un modulo que trata las señales analógicas recogidas, las une, y digitaliza para que el modulo transmisor pueda enviar via Bluetooth los datos hacia un receptor colocado en un área cercana. En el módulo hay una electrónica que ayuda a resolver problemas importantes como ruido o interferencias. Este receptor está conectado a un ordenador en el cual he desarrollado una aplicación que implementa el protocolo HCI y cuya funcionalidad es recoger los datos recibidos. Este programa es capaz de crear y gestionar conexiones Bluetooth entre dispositivos. El programa está preparado para que si las conexiones se cortan, se traten en la medida de lo posible los datos recogidos. Los datos se interpretarán y guardarán en un fichero .bin para posteriores usos, como graficaciones y análisis de parámetros. El programa está enteramente hecho en lenguaje Java y tiene un mecanismo de eventos que se activa cada vez que hay datos en el receptor, los recoge y los procesa con el fin de darles un trato posteriormente. Se eligió el formato .bin para los ficheros debido a su pequeño tamaño, ya que aunque sean más laboriosos de usar es mucho más eficiente que un .txt, que en este caso podría ocupar varios megabytes.

Slow-phase onset influence on waveform identification and foveation time measure in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder characterised by involuntary, conjugated ocular oscillations and its pathogenesis is still under investigation. This kind of nystagmus is termed congenital (or infantile) since it could be present at birth or it can arise in the first months of life. Most of CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, the image of a given target can still be stable during short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recording are routinely employed, allowing physicians to extract and analyse nystagmus main features such as waveform shape, amplitude and frequency. Using eye movement recording, it is also possible to compute estimated visual acuity predictors: analytical functions which estimates expected visual acuity using signal features such as foveation time and foveation position variability. Use of those functions extend the information from typical visual acuity measurement (e.g. Landolt C test) and could be a support for therapy planning or monitoring. This study focuses on detection of CN patients' waveform type and on foveation time measure. Specifically, it proposes a robust method to recognize cycles corresponding to the specific CN waveform in the eye movement pattern and, for those cycles, evaluate the exact signal tracts in which a subject foveates. About 40 eyemovement recordings, either infrared-oculographic or electrooculographic, were acquired from 16 CN subjects. Results suggest that the use of an adaptive threshold applied to the eye velocity signal could improve the estimation of slow phase start point. This can enhance foveation time computing and reduce influence of repositioning saccades and data noise on the waveform type identification.

Eye movement analysis in congenital nystagmus:concise parameters estimation

Along with other diseases that can affect binocular vision, reducing the visual quality of a subject, Congenital Nystagmus (CN) is of peculiar interest. CN is an ocular-motor disorder characterized by involuntary, conjugated ocular oscillations and, while identified more than forty years ago, its pathogenesis is still under investigation. This kind of nystagmus is termed congenital (or infantile) since it could be present at birth or it can arise in the first months of life. The majority of CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, the image of a given target can still be stable during short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recordings are routinely employed, allowing physicians to extract and analyze nystagmus main features such as waveform shape, amplitude and frequency. Use of eye movement recording, opportunely processed, allows computing "estimated visual acuity" predictors, which are analytical functions that estimate expected visual acuity using signal features such as foveation time and foveation position variability. Hence, it is fundamental to develop robust and accurate methods to measure both those parameters in order to obtain reliable values from the predictors. In this chapter the current methods to record eye movements in subjects with congenital nystagmus will be discussed and the present techniques to accurately compute foveation time and eye position will be presented. This study aims to disclose new methodologies in congenital nystagmus eye movements analysis, in order to identify nystagmus cycles and to evaluate foveation time, reducing the influence of repositioning saccades and data noise on the critical parameters of the estimation functions. Use of those functions extends the information acquired with typical visual acuity measurement (e.g., Landolt C test) and could be a support for treatment planning or therapy monitoring. © 2010 by Nova Science Publishers, Inc. All rights reserved.

Detection of foveation windows and analysis of foveation sequences in congenital nystagmus

Congenital nystagmus (CN) is an ocular-motor disorder characterised by involuntary, conjugated ocular oscillations, that can arise since the first months of life. Pathogenesis of congenital nystagmus is still under investigation. In general, CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, image stabilisation is still achieved during the short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recording are routinely employed, allowing physicians to extract and analyse nystagmus main features such as shape, amplitude and frequency. Using eye movement recording, it is also possible to compute estimated visual acuity predictors: analytical functions which estimates expected visual acuity using signal features such as foveation time and foveation position variability. Use of those functions add information to typical visual acuity measurement (e.g. Landolt C test) and could be a support for therapy planning or monitoring. This study focus on robust detection of CN patients' foveations. Specifically, it proposes a method to recognize the exact signal tracts in which a subject foveates, This paper also analyses foveation sequences. About 50 eyemovement recordings, either infrared-oculographic or electrooculographic, from different CN subjects were acquired. Results suggest that an exponential interpolation for the slow phases of nystagmus could improve foveation time computing and reduce influence of breaking saccades and data noise. Moreover a concise description of foveation sequence variability can be achieved using non-fitting splines. © 2009 Springer Berlin Heidelberg.

Radiotherapy Treatment Assessment using DCE-MRI

Abstract

The goal of modern radiotherapy is to precisely deliver a prescribed radiation dose to delineated target volumes that contain a significant amount of tumor cells while sparing the surrounding healthy tissues/organs. Precise delineation of treatment and avoidance volumes is the key for the precision radiation therapy. In recent years, considerable clinical and research efforts have been devoted to integrate MRI into radiotherapy workflow motivated by the superior soft tissue contrast and functional imaging possibility. Dynamic contrast-enhanced MRI (DCE-MRI) is a noninvasive technique that measures properties of tissue microvasculature. Its sensitivity to radiation-induced vascular pharmacokinetic (PK) changes has been preliminary demonstrated. In spite of its great potential, two major challenges have limited DCE-MRI’s clinical application in radiotherapy assessment: the technical limitations of accurate DCE-MRI imaging implementation and the need of novel DCE-MRI data analysis methods for richer functional heterogeneity information.

This study aims at improving current DCE-MRI techniques and developing new DCE-MRI analysis methods for particular radiotherapy assessment. Thus, the study is naturally divided into two parts. The first part focuses on DCE-MRI temporal resolution as one of the key DCE-MRI technical factors, and some improvements regarding DCE-MRI temporal resolution are proposed; the second part explores the potential value of image heterogeneity analysis and multiple PK model combination for therapeutic response assessment, and several novel DCE-MRI data analysis methods are developed.

I. Improvement of DCE-MRI temporal resolution. First, the feasibility of improving DCE-MRI temporal resolution via image undersampling was studied. Specifically, a novel MR image iterative reconstruction algorithm was studied for DCE-MRI reconstruction. This algorithm was built on the recently developed compress sensing (CS) theory. By utilizing a limited k-space acquisition with shorter imaging time, images can be reconstructed in an iterative fashion under the regularization of a newly proposed total generalized variation (TGV) penalty term. In the retrospective study of brain radiosurgery patient DCE-MRI scans under IRB-approval, the clinically obtained image data was selected as reference data, and the simulated accelerated k-space acquisition was generated via undersampling the reference image full k-space with designed sampling grids. Two undersampling strategies were proposed: 1) a radial multi-ray grid with a special angular distribution was adopted to sample each slice of the full k-space; 2) a Cartesian random sampling grid series with spatiotemporal constraints from adjacent frames was adopted to sample the dynamic k-space series at a slice location. Two sets of PK parameters’ maps were generated from the undersampled data and from the fully-sampled data, respectively. Multiple quantitative measurements and statistical studies were performed to evaluate the accuracy of PK maps generated from the undersampled data in reference to the PK maps generated from the fully-sampled data. Results showed that at a simulated acceleration factor of four, PK maps could be faithfully calculated from the DCE images that were reconstructed using undersampled data, and no statistically significant differences were found between the regional PK mean values from undersampled and fully-sampled data sets. DCE-MRI acceleration using the investigated image reconstruction method has been suggested as feasible and promising.

Second, for high temporal resolution DCE-MRI, a new PK model fitting method was developed to solve PK parameters for better calculation accuracy and efficiency. This method is based on a derivative-based deformation of the commonly used Tofts PK model, which is presented as an integrative expression. This method also includes an advanced Kolmogorov-Zurbenko (KZ) filter to remove the potential noise effect in data and solve the PK parameter as a linear problem in matrix format. In the computer simulation study, PK parameters representing typical intracranial values were selected as references to simulated DCE-MRI data for different temporal resolution and different data noise level. Results showed that at both high temporal resolutions (<1s) and clinically feasible temporal resolution (~5s), this new method was able to calculate PK parameters more accurate than the current calculation methods at clinically relevant noise levels; at high temporal resolutions, the calculation efficiency of this new method was superior to current methods in an order of 102. In a retrospective of clinical brain DCE-MRI scans, the PK maps derived from the proposed method were comparable with the results from current methods. Based on these results, it can be concluded that this new method can be used for accurate and efficient PK model fitting for high temporal resolution DCE-MRI.

II. Development of DCE-MRI analysis methods for therapeutic response assessment. This part aims at methodology developments in two approaches. The first one is to develop model-free analysis method for DCE-MRI functional heterogeneity evaluation. This approach is inspired by the rationale that radiotherapy-induced functional change could be heterogeneous across the treatment area. The first effort was spent on a translational investigation of classic fractal dimension theory for DCE-MRI therapeutic response assessment. In a small-animal anti-angiogenesis drug therapy experiment, the randomly assigned treatment/control groups received multiple fraction treatments with one pre-treatment and multiple post-treatment high spatiotemporal DCE-MRI scans. In the post-treatment scan two weeks after the start, the investigated Rényi dimensions of the classic PK rate constant map demonstrated significant differences between the treatment and the control groups; when Rényi dimensions were adopted for treatment/control group classification, the achieved accuracy was higher than the accuracy from using conventional PK parameter statistics. Following this pilot work, two novel texture analysis methods were proposed. First, a new technique called Gray Level Local Power Matrix (GLLPM) was developed. It intends to solve the lack of temporal information and poor calculation efficiency of the commonly used Gray Level Co-Occurrence Matrix (GLCOM) techniques. In the same small animal experiment, the dynamic curves of Haralick texture features derived from the GLLPM had an overall better performance than the corresponding curves derived from current GLCOM techniques in treatment/control separation and classification. The second developed method is dynamic Fractal Signature Dissimilarity (FSD) analysis. Inspired by the classic fractal dimension theory, this method measures the dynamics of tumor heterogeneity during the contrast agent uptake in a quantitative fashion on DCE images. In the small animal experiment mentioned before, the selected parameters from dynamic FSD analysis showed significant differences between treatment/control groups as early as after 1 treatment fraction; in contrast, metrics from conventional PK analysis showed significant differences only after 3 treatment fractions. When using dynamic FSD parameters, the treatment/control group classification after 1st treatment fraction was improved than using conventional PK statistics. These results suggest the promising application of this novel method for capturing early therapeutic response.

The second approach of developing novel DCE-MRI methods is to combine PK information from multiple PK models. Currently, the classic Tofts model or its alternative version has been widely adopted for DCE-MRI analysis as a gold-standard approach for therapeutic response assessment. Previously, a shutter-speed (SS) model was proposed to incorporate transcytolemmal water exchange effect into contrast agent concentration quantification. In spite of richer biological assumption, its application in therapeutic response assessment is limited. It might be intriguing to combine the information from the SS model and from the classic Tofts model to explore potential new biological information for treatment assessment. The feasibility of this idea was investigated in the same small animal experiment. The SS model was compared against the Tofts model for therapeutic response assessment using PK parameter regional mean value comparison. Based on the modeled transcytolemmal water exchange rate, a biological subvolume was proposed and was automatically identified using histogram analysis. Within the biological subvolume, the PK rate constant derived from the SS model were proved to be superior to the one from Tofts model in treatment/control separation and classification. Furthermore, novel biomarkers were designed to integrate PK rate constants from these two models. When being evaluated in the biological subvolume, this biomarker was able to reflect significant treatment/control difference in both post-treatment evaluation. These results confirm the potential value of SS model as well as its combination with Tofts model for therapeutic response assessment.

In summary, this study addressed two problems of DCE-MRI application in radiotherapy assessment. In the first part, a method of accelerating DCE-MRI acquisition for better temporal resolution was investigated, and a novel PK model fitting algorithm was proposed for high temporal resolution DCE-MRI. In the second part, two model-free texture analysis methods and a multiple-model analysis method were developed for DCE-MRI therapeutic response assessment. The presented works could benefit the future DCE-MRI routine clinical application in radiotherapy assessment.

Pre-processing for noise detection in gene expression classification data

Due to the imprecise nature of biological experiments, biological data is often characterized by the presence of redundant and noisy data. This may be due to errors that occurred during data collection, such as contaminations in laboratorial samples. It is the case of gene expression data, where the equipments and tools currently used frequently produce noisy biological data. Machine Learning algorithms have been successfully used in gene expression data analysis. Although many Machine Learning algorithms can deal with noise, detecting and removing noisy instances from the training data set can help the induction of the target hypothesis. This paper evaluates the use of distance-based pre-processing techniques for noise detection in gene expression data classification problems. This evaluation analyzes the effectiveness of the techniques investigated in removing noisy data, measured by the accuracy obtained by different Machine Learning classifiers over the pre-processed data.

Modelling tyre-road noise with data mining techniques

The research aimed to establish tyre-road noise models by using a Data Mining approach that allowed to build a predictive model and assess the importance of the tested input variables. The data modelling took into account three learning algorithms and three metrics to define the best predictive model. The variables tested included basic properties of pavement surfaces, macrotexture, megatexture, and uneven- ness and, for the first time, damping. Also, the importance of those variables was measured by using a sensitivity analysis procedure. Two types of models were set: one with basic variables and another with complex variables, such as megatexture and damping, all as a function of vehicles speed. More detailed models were additionally set by the speed level. As a result, several models with very good tyre-road noise predictive capacity were achieved. The most relevant variables were Speed, Temperature, Aggregate size, Mean Profile Depth, and Damping, which had the highest importance, even though influenced by speed. Megatexture and IRI had the lowest importance. The applicability of the models developed in this work is relevant for trucks tyre-noise prediction, represented by the AVON V4 test tyre, at the early stage of road pavements use. Therefore, the obtained models are highly useful for the design of pavements and for noise prediction by road authorities and contractors.

ECG Noise Removal using GA tuned Sign-Data Least Mean Square Algorithm

Adaptive filter is a primary method to filter Electrocardiogram (ECG), because it does not need the signal statistical characteristics. In this paper, an adaptive filtering technique for denoising the ECG based on Genetic Algorithm (GA) tuned Sign-Data Least Mean Square (SD-LMS) algorithm is proposed. This technique minimizes the mean-squared error between the primary input, which is a noisy ECG, and a reference input which can be either noise that is correlated in some way with the noise in the primary input or a signal that is correlated only with ECG in the primary input. Noise is used as the reference signal in this work. The algorithm was applied to the records from the MIT -BIH Arrhythmia database for removing the baseline wander and 60Hz power line interference. The proposed algorithm gave an average signal to noise ratio improvement of 10.75 dB for baseline wander and 24.26 dB for power line interference which is better than the previous reported works

A new algorithm for OFDM joint data detection and phase noise cancellation

This paper proposes a new iterative algorithm for OFDM joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the problem of "overfitting" such that the iterative approach may converge to a trivial solution. Although it is essential for this joint approach, the overfitting problem was relatively less studied in existing algorithms. In this paper, specifically, we apply a hard decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the phase noise, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical simulations are also given to verify the proposed algorithm.

OFDM joint data detection and phase noise cancellation based on minimum mean square prediction error

This paper proposes a new iterative algorithm for orthogonal frequency division multiplexing (OFDM) joint data detection and phase noise (PHN) cancellation based on minimum mean square prediction error. We particularly highlight the relatively less studied problem of "overfitting" such that the iterative approach may converge to a trivial solution. Specifically, we apply a hard-decision procedure at every iterative step to overcome the overfitting. Moreover, compared with existing algorithms, a more accurate Pade approximation is used to represent the PHN, and finally a more robust and compact fast process based on Givens rotation is proposed to reduce the complexity to a practical level. Numerical Simulations are also given to verify the proposed algorithm. (C) 2008 Elsevier B.V. All rights reserved.

OFDM joint data detection and phase noise cancellation for constant modulus modulations

This correspondence proposes a new algorithm for the OFDM joint data detection and phase noise (PHN) cancellation for constant modulus modulations. We highlight that it is important to address the overfitting problem since this is a major detrimental factor impairing the joint detection process. In order to attack the overfitting problem we propose an iterative approach based on minimum mean square prediction error (MMSPE) subject to the constraint that the estimated data symbols have constant power. The proposed constrained MMSPE algorithm (C-MMSPE) significantly improves the performance of existing approaches with little extra complexity being imposed. Simulation results are also given to verify the proposed algorithm.