MainWindow.xaml

<Window x:Class="Default_MVVM.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:dxg="http://schemas.devexpress.com/winfx/2008/xaml/grid"
        xmlns:dxe="http://schemas.devexpress.com/winfx/2008/xaml/editors"
        xmlns:local="clr-namespace:Default_MVVM"
        Title="MainWindow" Height="550" Width="525">
    <Grid>
        <Grid.RowDefinitions>
            <RowDefinition MaxHeight="30"/>
            <RowDefinition/>
        </Grid.RowDefinitions>
        <TextBlock Text="DxGrid" FontSize="20" FontWeight="ExtraBold"/>
        <dxg:GridControl x:Name="grid" ItemsSource="{Binding Records}" Grid.Row="1">
            <dxg:GridControl.Columns>
                <dxg:GridColumn FieldName="Text"/>
                <dxg:GridColumn FieldName="Number" FilterPopupMode="Custom">
                    <dxg:GridColumn.CustomColumnFilterPopupTemplate>
                        <DataTemplate>
                            <ScrollViewer Focusable="False" MaxHeight="350">
                                <StackPanel>
                                    <dxe:ListBoxEdit 
                                        ItemsSource="{Binding RelativeSource={RelativeSource Mode=FindAncestor, AncestorType=dxg:GridControl},
                                        Converter={local:FilterPopupConverter}}"
                                                 ValueMember="Number" DisplayMember="Number">
                                        <dxe:ListBoxEdit.ItemTemplate>
                                            <DataTemplate>
                                                <StackPanel Orientation="Horizontal">
                                                    <Image Source="{Binding Image}" Margin="3,3,3,3" Width="70" Height="70"/>
                                                    <TextBlock Text="{Binding Number}" Margin="3,3,3,3" VerticalAlignment="Center"/>
                                                </StackPanel>
                                            </DataTemplate>
                                        </dxe:ListBoxEdit.ItemTemplate>
                                        <dxe:ListBoxEdit.EditValue>
                                            <MultiBinding Converter="{local:CriteriaOperatorConverter}" Mode="OneWayToSource">
                                                <Binding Path="CustomColumnFilter"
                                                 RelativeSource="{RelativeSource TemplatedParent}"/>
                                                <Binding Path="(dxe:BaseEdit.OwnerEdit).IsPopupOpen"
                                                 RelativeSource="{RelativeSource TemplatedParent}"/>
                                            </MultiBinding>
                                        </dxe:ListBoxEdit.EditValue>
                                    </dxe:ListBoxEdit>
                                </StackPanel>
                            </ScrollViewer>
                        </DataTemplate>
                    </dxg:GridColumn.CustomColumnFilterPopupTemplate>
                </dxg:GridColumn>
                <dxg:GridColumn FieldName="Image">
                    <dxg:GridColumn.CellTemplate>
                        <DataTemplate>
                            <Image Source="{Binding RowData.Row.Image}" Margin="5,5,5,5"/>
                        </DataTemplate>
                    </dxg:GridColumn.CellTemplate>
                </dxg:GridColumn>
            </dxg:GridControl.Columns>
        </dxg:GridControl>
    </Grid>
</Window>