Hi Lanna - Thank you for posting the last version of that image. It's large enough to see detail (including noise) in the image, and it contains the EXIF information that I needed to understand the problem you are facing.
FYI, even though you camera was set on full automatic mode, it still recorded all the exposure information:
Camera Maker: Panasonic
Camera Model: DMC-TZ7
Image Date: 2010-11-05 22:42:57 +0000
Focal Length: 4.7mm (35mm equivalent: 29mm)
Aperture: f/3.4
Exposure Time: 0.013 s (1/80)
ISO equiv: 80
Exposure Bias: none
Metering Mode: Matrix
Exposure: program (Auto)
White Balance: Auto
Flash Fired: No (enforced)
Orientation: Normal
Color Space: sRGB
GPS Coordinate: undefined, undefined
Software: Adobe Photoshop CS6 (Windows)
I was worried that you or the camera might have increased the ISO to high values to take this shot. If this had happened, that would immediately explain excess digital noise in the shadows. However, the above information tells us that this shot was taken at ISO = 80, a nice low value that will produce about as little grain as your camera is capable of. Under these lighting conditions, your camera (which has very good vibration reduction) selected a very appropriate exposure time: 1/80th of a second. It also selected a very appropriate f-stop: 3.4 (ie, nearly wide open). This is again very appropriate and just about exactly what I would have used if I had the camera set on manual mode.
The next thing I was worried about was that you (or the camera) had inadvertently underexposed the photo, thereby requiring excessive amounts of brightening in post processing. The histogram of this image (see 1st attachment) shows that it is almost perfectly exposed -- the peak is perfectly centered on the x-axis and none of the extreme pixels (ie, very bright or very dark) are beyond the limits of the sensor in your camera.
However, the histogram also tells us that this was originally a very low contrast image. Other images that you have posted show that you prefer a much more contrasty image. I would, too. However, increasing the contrast, as you pointed out, increases the noise and blotchy nature of the image.
Thus, it appears that neither you, nor the camera made any technical mistakes or mis-judged anything.
So, the question is what to do about the digital noise. Like you, I tried processing that image to increase the contrast, but I also applied various noise reduction techniques that you might not have tried. The results were not encouraging (see 2nd and 3rd attachments).
It has been suggested that you have the camera record images in RAW format instead of only JPGs. This is always a good idea, but, to be honest, even if your camera had that capability, in my experience, it wouldn't help all that much.
The real root cause of the noise problem arises because of simple physics: If you compare a full frame DSLR (ie, large sensor, large lens) to a tiny point and shoot (ie, tiny sensor, tiny lens), each pixel on the P&S's sensor is much smaller than the pixels on DSLRs, so, for a given exposure, they receive many fewer photons. Since their arrival is randomly distributed, this means that small P&S cameras are vastly more susceptible to digital noise than their large DSLR cousins.
I understand your preference for a small camera / housing, but I think that if you want to keep the digital noise to an absolute minimum, you need to move to a larger format camera. The best would be a full frame DSLR, but in the past 2 or 3 years, there have been major improvements in digital noise, so even a modern APS-sized DSLR would likely give you all the noise performance that you require.
Sorry I can't be more encouraging.
Regards,
Tom