You could easily build something up using GPUImage. It comes with a huge set of blurs, noise generators and filters.. You can connect them together in sequence and build up complex GPU accelerated effects. 
To give you an good starting point. Here's a quick dirty prototype of a function that uses GPUImage to do something like what you want. If you set 'orUseNoise' to YES it will create a blurred image based on perlin noise INSTEAD if the image. Tweak the values pointed out to change the desired effect.
- (UIImage *)blurWithGPUImage:(UIImage *)sourceImage orUseNoise:(bool) useNoise {
    GPUImagePicture *stillImageSource = [[GPUImagePicture alloc] initWithImage:sourceImage];
    GPUImageGaussianBlurFilter *gaussFilter = [[GPUImageGaussianBlurFilter alloc] init];
    [gaussFilter setBlurRadiusInPixels:6];                                      //<<-------TWEAK
    [gaussFilter setBlurPasses:1];                                              //<<-------TWEAK
    if(useNoise) {
        GPUImagePerlinNoiseFilter* perlinNouse = [[GPUImagePerlinNoiseFilter alloc] init];
        [perlinNouse setColorStart:(GPUVector4){1.0, 1.0, 1.0f, 1.0}];          //<<-------TWEAK
        [perlinNouse setColorFinish:(GPUVector4){0.5,0.5, 0.5f, 1.0}];          //<<-------TWEAK
        [perlinNouse setScale:200];                                             //<<-------TWEAK
        [stillImageSource addTarget:perlinNouse];
        [perlinNouse addTarget:gaussFilter];
    } else {
        [stillImageSource addTarget:gaussFilter];
    }
    [gaussFilter useNextFrameForImageCapture];
    [stillImageSource processImage];
    UIImage *outputImage = [gaussFilter imageFromCurrentFramebuffer];
    // Set up output context.
    UIGraphicsBeginImageContext(self.view.frame.size);
    CGContextRef outputContext = UIGraphicsGetCurrentContext();
    // Invert image coordinates
    CGContextScaleCTM(outputContext, 1.0, -1.0);
    CGContextTranslateCTM(outputContext, 0, -self.view.frame.size.height);
    // Draw base image.
    CGContextDrawImage(outputContext, self.view.frame, outputImage.CGImage);
    // Apply tint
    CGContextSaveGState(outputContext);
    UIColor* tint = [UIColor colorWithWhite:1.0f alpha:0.6];                    //<<-------TWEAK
    CGContextSetFillColorWithColor(outputContext, tint.CGColor);
    CGContextFillRect(outputContext, self.view.frame);
    CGContextRestoreGState(outputContext);
    // Output image
    outputImage = UIGraphicsGetImageFromCurrentImageContext();
    UIGraphicsEndImageContext();
    return outputImage;
}
This is a simple stack of: 
GPUImagePicture -> GPUImagePerlinNoiseFilter -> GPUImageGaussianBlurFilter
..with a bit of handling code to make into an image properly.
You can try changing the stack to use some of the many other filters.
NOTE: Even if you use the noise instead of the image. You will still need to provide an image until you cut that part out.