<Window x:Class="WpfAppImageBase64.MainWindow"
          xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
          xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
          xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
          xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
          xmlns:local="clr-namespace:WpfAppImageBase64"
          mc:Ignorable="d"
          Title="MainWindow" Height="450" Width="800">
     <Grid>

          <Image x:Name="MyControlImg"/>

     </Grid>
</Window>

using System;
using System.Drawing;
using System.Drawing.Imaging;
using System.IO;
using System.Windows;
using System.Windows.Media.Imaging;

namespace WpfAppImageBase64
{
     public partial class MainWindow : Window
     {
          public MainWindow()
          {
               InitializeComponent();

               string imageBase64 = "Qk04JAAAAAAAADYAAAAoAAAAYAAAACAAAAABABgAAAAAAAIk......."; // image in base 64
               // Note! Please download full example code to see correct imageBase64 value
               try
               {
                    var image = Base64StringToImage(imageBase64);
                    MyControlImg.Source = ConvertImageToBitmapImage(image);
               }
               catch (Exception)
               {
               }
          }

          public static Image Base64StringToImage(string base64String)
          {
               byte[] byteBuffer = Convert.FromBase64String(base64String);
               MemoryStream memoryStream = new MemoryStream(byteBuffer);
               memoryStream.Position = 0;
               return Image.FromStream(memoryStream);
          }

          public static BitmapImage ConvertImageToBitmapImage(Image image)
          {
               using (var memory = new MemoryStream())
               {
                    image.Save(memory, ImageFormat.Bmp);
                    memory.Position = 0;

                    var bitmapImage = new BitmapImage();
                    bitmapImage.BeginInit();
                    bitmapImage.StreamSource = memory;
                    bitmapImage.CacheOption = BitmapCacheOption.OnLoad;
                    bitmapImage.EndInit();

                    return bitmapImage;
               }
          }
     }
}