How implement background process for controller in angularjs?

You can use angularjs service to remember this "Process" of making an api call and getting the data from it . here is a simple implementation.

the whole idea here is to create a angular service which will make an api call, store the data aswell as the state of the data, so that it can be accessed from other modules of angularjs. note that since angularjs services are singleton that means all of their state will be preserved.

app.service('searchService', function() {
    this.searchState={
     loading: false,
     data: null,
     error: null
    }
    this.fetchSearchResults = function(key){
    // call api methods to get response
    // can be via callbacks or promise. 

     this.searchState.loading=true;

     someMethodThatCallsApi(key)
      .then(function(success){
        this.searchState.loading=false;
        this.searchState.data=success;
        this.searchState.error=null
       })
      .catch(function(error){
       this.searchState.loading=false;
       this.searchState.data=null;
       this.searchState.error=error
      });

    }
    this.getState = function(){
      return this.searchState
    }
});

// in your controller

app.controller('searchController',function(searchService){
   // in your initialization function call the service method.
   var searchState = searchService.getState();
   // search state has your loading variables. you can easily check 
   // and procede with the logic.
   searchState.loading // will have loading state
   searchState.data // will have data
   searchState.error // will have error if occured.
});

Even if you navigate from pages. the angular service will preserve the state and you can get the same data from anywhere in the application. you simply have to inject the service and call the getter method.

Based on the question, (a little bit more context or code would help answers be more targeted), when considering async operations within angularJS, its always advisable to use getters and setters within service to avoid multiple REST calls.

Please note - Services are singletons, controller is not.

for eg:

angular.module('app', [])
   .controller('ctrlname', ['$scope', 'myService',  function($scope, myService){

    myService.updateVisitCount();
    $scope.valueFromRestCall = myService.myGetterFunctionAssociated(param1, param2);

    //Use $scope.valueFromRestCall to your convinience.

   }]

   .service('myService', ['$http', function($http){

        var self = this;
        self.numberOfVisits = 0;
        self.cachedResponse = null;

        self.updateVisitCount = function(){
            self.numberOfVisits+=1;
        }

        self.myGetterFunctionAssociated = function(param1, param2){
            if self.cachedResponse === null || self.numberOfVisits === 0 {
                return $http.get(url).then(function(response){
                    self.cachedResponse = response;
                    return response;
                });
            }
            else {
                      return self.cachedResponse;
                 }
        }

        return {
            updateVisitCount: function(){
                 self.udpateVisitCount();
            },
            myGetterFunctionAssociated : function(param1, param2){
                 return self.myGetterFunctionAssociated(param1, param2);
            }
        }

   }]