Intro
Technically it can be done using all of your possibilities, I will rank them by the difficulty from low to hard, I will even few more possibilities. Also, I wrote much more extensive ARTICLE for my blog.
PhoneGap/Cordova + jQuery Mobile (Low difficulty)
Phonegap is what you need here, jQuery Mobile is only for the UI. Still this combination is very easy to implement together and there are a lot of working examples. Phonegap serves as a wrapper for HTML5/JS/CSS and it will give you an access to mobile phone functionalists. Phonegap will be used to take a picture and jQM will be used to modifications.
Here’s a rather new PhoneGap + jQuery Mobile tutorial. If you want to see a MAcOS version of that article than take a look here.
Take a look HERE if you want to find a good source of information regarding differences between jQuery and jQuery Mobile a lot lot more.
PhoneGap/Cordova + Sencha Touch (Medium/Hard difficulty)
Unlike jQM, Sencha Touch is a bit harder (or a lot harder, depending on your javascript knowledge) to learn, especially if you don’t have a good background knowledge with javascript or don’t have a license for Sencha Touch designer tool. Go this road only if you have have enough time to learn something new. Sencha Touch version 2 has its own app wrapper so Phonegap is no longer needed.
If you want to find out more take a look at this ARTICLE that discuss the difference between jQuery Mobile and Sencha Touch.
Titanium Appcelerator (Medium difficulty)
Unlike previous two options, Titanium works a little bit different. Where jQM and Sencha are used to create a hybrid mobile app, Titanium appcelerator is used to create a native app from javascript code. Not too difficult to master, js code is pretty simple to be frank. While fast development tool it will be harder to properly style your native app (it’s much easier process when building it native from scratch).
Inter App Framework / ex jqMoby (Low difficulty)
This framework is almost old as jQuery Mobile and now it is owned by Intel. Like Sencha Touch main goal of this framework is hybrid mobile app development and it works great. It is optimized for Android and iOS so expect faster execution then jQuery Mobile, also like Sencha Touch this framework has its own native app wrapper. Of course there are few bad sides of this framework like horrible documentation (at least during the point of writing this article). If you want to find more about this framework take a look at this ARTICLE.
Kendo UI (Low difficulty)
Excelent alternative to jQuery Mobile. Better, faster in any way. There’s only one problem, it is a commercial product. It will cost you cca 200 USD.
Find more information here.
PhoneJS (Low difficulty)
Another excellent alternative to jQuery Mobile and Kendo UI. Much faster then jQuery Mobile, on the same level like Kendo UI. It has a great documentation, one of the best I so up to today.
Find more information here.
Read about it HERE.
Honorable mention
Goes to Rhomobile. Similar to Phonegap/Cordova but less used.
From the perspective of developing time it is faster to create a hybrid app then a native one. In your case, if you have a Java/Objective C knowlede stick with native app. No matter how much time you sink into hybrid app it will be good or fast enough.
EDIT :
Here’s an Phonegap + jQuery Mobile example: http://therockncoder.blogspot.com/2012/07/jquery-mobile-phonegap-and-camera.html, there you will find a github link for Android and iOS implementation.
If you have never used jQuery then stick with Dawson Toth Titanium example. But if possible stick with jQuery Mobile.
UPDATE 1
You might also be interested in the open source PropertyCross project which demonstrates the same application implemented with a range of cross-platform frameworks (including Sencha, jQM and PhoneGap).
UPDATE 2
I have spent last few weeks review other HTML5 mobile frameworks. My comment can be found here and here.