<div class="bgdiv“ style="background-image: url('../test.png'); background-repeat: no-repeat; background-size: cover;">
     <div style="position: inherit; z-index: 10;">文字部分</div>
</div>


.bgdiv{ 
    height:100%;
    position: relative;
    background: inherit;
    padding:1px;
    box-sizing:border-box;
    z-index:1;
}
.bgdiv::after{
    content: "";
    width:100%;
    height:100%;
    position: absolute;
    left:0;
    top:0;
    background: inherit;
    filter: blur(3px);
    z-index: 2;
}