I took a look at the channels, and the blue channel struck me as being decent for a mask in this case. It provides for the darkest background, and in this image doesn't have as much noise as is normally associated with the blue channel.
Then I went to Image> Calculations. I used the blue channel for both channel settings, and set the blend mode to 'overlay'. This created a new alpha channel that had more contrast than the blue channel.
Then I went to Image> Adjustments> Threshold, adjusting the threshold setting to make as much of the basket as possible white, and as much of the background as possible black.
With my mask complete, I ctrl-clicked on it to load it as a selection. Then I clicked on the RGB channel and switched over to the layers pallette. I copied the selection to a new layer.
My mask included the white note underneath the basket, so I selected it with the marquee tool and deleted it.
There was still a bit of red showing up as a reflection off the basket. I went to Image> Adjustments> Hue/Saturation, chose 'reds' from the drop-down menu, and desaturated it until it blended nicely with the rest of the basketry.
Lastly, I deleted the background layer, and saved the file as a .gif, which preserves transparency. I could have saved it as a PNG, which also preserves transparency. But the file is small enough to be saved as a .gif, and the .gif format is still more readily accepted on the web. The result is a file that will blend with any background you put it on. However, as the background was initially fairly dark, it will blend better on darker backgrounds.
Hope this helps.
-Medley.