Removing background from a sprite

Here's a simple editor script I use to remove a color from images without opening an external editor. You can drag multiple files into the object field to batch alpha-fy images. To use this script create a C# file called ImageTool.cs and place it in a folder called Editor. Then open Window/Tools/Alpha-fy Images.

 using UnityEngine;
 using UnityEditor;
 using System.IO;
 using System;
 using System.Collections.Generic;
 
 public class ImageTool: EditorWindow
 {
     Texture2D img;
     Texture2D newImg;
     Color colorToRemove = Color.red;
     public static ImageTool win;    
     
     [MenuItem("Window/Tools/Alpha-fy Images")]
     static void Init () 
     {
         win = ScriptableObject.CreateInstance( typeof(ImageTool) ) as ImageTool;
         win.ShowUtility();            
     }
     
     void OnGUI()
     {
         GUILayout.BeginHorizontal();
         
             /** Toolbar **/
             GUILayout.BeginVertical();
                 img = (Texture2D)EditorGUILayout.ObjectField(img, typeof(Texture2D), false, GUILayout.MinWidth(128), GUILayout.MinHeight(128), GUILayout.MaxWidth(128), GUILayout.MaxHeight(128));
             
                 colorToRemove = EditorGUILayout.ColorField(colorToRemove, GUILayout.MaxWidth(128));
                 
                 if(GUILayout.Button("Preview", GUILayout.MinWidth(128), GUILayout.MinHeight(32), GUILayout.MaxWidth(128), GUILayout.MaxHeight(128)))
                     newImg = RemoveColor(colorToRemove, img);
                 
                 if(GUILayout.Button("Alpha-fy All", GUILayout.MinWidth(128), GUILayout.MinHeight(32), GUILayout.MaxWidth(128), GUILayout.MaxHeight(128)))
                     RemoveColor(colorToRemove, (UnityEngine.Object[])Selection.GetFiltered(typeof(Texture2D), SelectionMode.Assets) );
                     
             GUILayout.EndVertical();
             
             GUILayout.BeginVertical();
                 GUILayout.Label("Selected Files", EditorStyles.boldLabel);
                 foreach(Texture2D selected in Selection.GetFiltered(typeof(Texture2D), SelectionMode.Assets) )
                 {
                     GUILayout.Label(selected.name);
                 }
             GUILayout.EndVertical(); 
             
             /** Image Display **/    
         GUILayout.BeginVertical();
             GUILayout.Label("Preview", EditorStyles.boldLabel);
             if(newImg)
             {        
                 GUILayout.Label(newImg);        
             }
         GUILayout.EndVertical();
         
         GUILayout.EndHorizontal();
             
     }
     
     void RemoveColor(Color c, UnityEngine.Object[] imgs)
     {
         if(!Directory.Exists("Assets/AlphaImages/"))
         {
             Directory.CreateDirectory("Assets/AlphaImages/");
         }
         float inc = 0f;
         foreach(Texture2D i in imgs)
         {
             inc++;
             if(EditorUtility.DisplayCancelableProgressBar(
                 "Playin' With Pixels",
                 "Seaching for Color Matches",
                 ( (float)inc/(float)imgs.Length) ) )
                 {
                     break;
                 }
                 
             ssEditorTools.MaxImportSettings(i);        
             Color[] pixels = i.GetPixels(0, 0, i.width, i.height, 0);
             for(int p = 0; p < pixels.Length; p++)
             {            
                 if(pixels[p] == c)
                     pixels[p] = new Color(0,0,0,0);
             }
                             
             Texture2D n = new Texture2D(i.width, i.height);
             n.SetPixels(0, 0, i.width, i.height, pixels, 0);
             n.Apply();
             
             byte[] bytes = n.EncodeToPNG();
             File.WriteAllBytes("Assets/AlphaImages/" + i.name + "_alpha.png", bytes);
         }
         
         EditorUtility.ClearProgressBar();
 
         AssetDatabase.SaveAssets();
         AssetDatabase.Refresh();
     }    
     
     Texture2D RemoveColor(Color c, Texture2D i)
     {
         ssEditorTools.MaxImportSettings(i);        
 
         Color[] pixels = i.GetPixels(0, 0, i.width, i.height, 0);
 
         for(int p = 0; p < pixels.Length; p++)
         {
             if(EditorUtility.DisplayCancelableProgressBar(
                 "Playin' With Pixels",
                 "Seaching for Color Matches",
                 ( (float)p/pixels.Length) ) )
                 {
                     break;
                 }
                 
             if(pixels[p] == c)
                 pixels[p] = new Color(0,0,0,0);
         }
                         
         Texture2D n = new Texture2D(i.width, i.height);
         n.SetPixels(0, 0, i.width, i.height, pixels, 0);
         n.Apply();
         EditorUtility.ClearProgressBar();
         return(n);
     }
 }

Hello smallB, I may have come a few years too late but I though I would contribute. Assuming you have Photoshop, you can cut out or erase the white from you artwork.

Duplicate your existing layer with the spaceship on (CMD+J or ctrl+J) - Delete your white space either buy selecting or using the eraser on your new layer. (make sure to hide or mask the original layer, otherwise you wont see what you have deleted)

You can either save for web or Save as a .PNG. Make sure to retain the alpha, keep it at 24 bit.

Let me know if this helps!