Brighten the blurred image, and reduce the contrast. I usually use levels rather than brightness/contrast because I think it gives you more control.
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In Photoshop 5.5 and up you can create an adjustment layer (the half black half white circle icon). The advantage of using an adjustment layer is that you can alway modify it's values (by double clicking the layer's icon).
Group the adjustment layer to the blurred layer, so that the levels affects only that layer. You group layers this way: while pressing the Alt key, point the mouse to the line between two layers, when the pointer changes to , click to group these two layers.
If your application doesn't have such a feature, just apply regular Levels filter to the layer.
To brighten using levels, move the right most triangle (under the graph) to the left. To change contrast move the middle triangle (move left=less contrast).